International narcotics trade, foreign aid, and enforcement.
Oladi, Reza ; Gilbert, John
I. INTRODUCTION
It is widely accepted that the problems that a country may face as
a direct result of narcotics-related activities are numerous. (1)
Moreover, drug production and trade are intimately tied to other serious
international concerns, notably the financing of insurgencies and
terrorist activities (Shughart 2006; Keefer, Loayza, and Soares 2008,
Intriligator 2010; Piazza 2011). A prime example is the involvement of
the Taliban in Afghanistan in the production and trafficking of heroin
(see Blanchard 2009; Clemens 2013a, 2013b). Similar issues are observed
in Colombia and Mexico. Hence, the indirect costs of narcotics-related
activities are also substantial. Nonetheless, the enforcement of
prohibitions on the production, consumption, and movement of narcotics
remains among the most controversial issues in international relations,
not least because the global response has met with somewhat limited
success. (2)
Even taking the objective of reducing global consumption of
narcotics as given, it is unclear which of the available policy tools
are likely to be the most effective at meeting the objective. The
consumption and distribution in narcotics importing countries can be
targeted directly, although the history of the past one and a half
centuries indicates that it is very difficult. Alternatively, and more
realistically, the supply side can be targeted. Law enforcement
authorities in narcotics-exporting countries can be used to eradicate
production facilities and to interdict trafficking, and alternative
production activities can be encouraged by providing technical
assistance, or by direct subsidization.
In all cases involving the supply side, however, it must be
recognized that the global production of narcotics is concentrated in
developing economies. Many of these countries lack the enforcement
resources to engage effectively against well-funded producers and
well-armed traffickers and their supporting terrorist and rebel groups.
Therefore, foreign aid to finance law enforcement activities is
essential. (3) Alternative development policies may also be supported
through foreign technical assistance, or by directing foreign aid toward
alternative production subsidies. The effects of these policies on
narcotics-exporting economies have not, however, been adequately
addressed in the literature.
Our work adds a new dimension to the existing literature on the
economics of narcotics. (4) We construct a theoretical model that
explores the effects of foreign financing of anti-narcotics enforcement
activities in narcotics-producing/exporting countries, along with other
potential policy interventions. While previous literature has taken a
partial equilibrium approach to analyzing related issues, our work
differs substantially in adopting general equilibrium methods. As Martin
and Symansky (2006) note, opium production in Afghanistan, for example,
accounted for approximately 27% of economic activity in 2005/2006. Given
this fact, substantial general equilibrium effects must be present, and
deserve full exploration. We focus attention on the consequences of the
multitude of severe distortions that narcotics production and
enforcement introduce to factor markets. We envisage an economy where
workers engage in both licit and illicit activities, are paid a premium
for the risk of incarceration (or seizure of their marginal product)
involved in the latter, and a nonproductive law enforcement sector uses
real resources to combat illicit activity. Our work draws on a number of
strands of economic theory, including tied aid, factor market
distortions, dual economies, illicit markets, and law enforcement.
A number of important new results emerge from our analysis. Foreign
aid will increase enforcement activity and will generally lower
narcotics production. The more market power the narcotics-producing
country has, the less effective foreign aid will be, however. In fact,
aid intended for anti-narcotics enforcement may effectively be siphoned
into the wages of narcotics workers. Paradoxically, under some
specifications of enforcement, it is even possible that aid directed to
anti-narcotics enforcement could increase illicit production. We also
show that an increase in foreign aid that finances anti-narcotics
activities can lower welfare in the recipient country under plausible
conditions. On the other hand, an improvement in the technology used in
the licit sector, that is, technology transfer in this context, is
unambiguously welfare improving (assuming that it does not spill over
into increased productivity in narcotics). Finally, we are able to
characterize conditions under which the production of narcotics is more
efficiently targeted by financing enforcement relative to technology
transfer.
The structure of the paper is as follows. In the next section, we
present a brief overview of some important characteristics of global
narcotics markets. In Section III we present our basic model framework.
In Sections IV and V we explore the implications of foreign aid to
enforcement and alternative development strategies, respectively. In
Section VI, we consider alternative characterizations of the enforcement
mechanism. Concluding comments and avenues for future research follow.
II. OVERVIEW OF THE GLOBAL NARCOTICS MARKET
Before moving on to our formal model, we outline three key facts
relating to our analysis: (1) The majority of narcotics production takes
place in developing economies; (2) the majority of consumption takes
place in developed economies, implying a significant volume of
international trade; and (3) foreign aid is used to finance
anti-narcotics enforcement in developing countries.
Concerning the global narcotics supply, Table 1 shows the
cultivation and production estimates for major drug-producing/exporting
countries in 2010. Afghanistan, Myanmar, and Mexico are the major
producers of opium, with Afghanistan believed to have a 77% share of
global production. The main producers of cocaine are located on the
Pacific Coast of South America: Colombia, Peru, and Bolivia. While
Colombia dominates the market, the shares of Bolivia and Peru are not
insubstantial, at roughly 13% and 35%, respectively, in 2008 (UNODC
[United Nations Office on Drugs and Crime] 2012). In contrast to cocaine
and opium, the production of cannabis is much less concentrated.
However, Morocco and Mexico are among the major producing countries. The
most important observation from Table 1 is that 100% of global cocaine
and opium production takes place in nine developing countries. On the
top of the short list of global suppliers are Afghanistan and Colombia.
On the demand side, Table 2 presents the latest estimates of
prevalence rates for three categories of narcotics. Although drug abuse
is a global problem, the prevalence of drug use for each type of
narcotic differs substantially across regions, in particular for opiates
and cocaine. While the prevalence rate for opiates in the Americas is
0.2, the estimated rate for cocaine is 1.2 (using the best estimate).
The picture for Asia is the reverse. The prevalence rates for cocaine
and opiates are about 0.05 and 0.4, respectively. On the other hand,
Africa and Europe are in-between cases. This regionalized consumption
pattern perhaps reflects variations in consumer preferences, but is also
likely due to the proximity of production locations to consumers and,
therefore, lower trafficking costs (i.e., transportation costs, risk,
and so on).
While prevalence rates give us an indication of the extent of drug
use, the number of drug consumers is a better indicator of total demand
size. Here we observe that no drug-producing countries are even close to
being major consuming countries, while the Western world accounts for a
large share of the total narcotics market. Table 2 indicates that
Central and Western Europe and North America combined account for 14% of
global consumers of opiates and 56% of the world's cocaine
consumers. Within Asia, China is a large consumer/importer of opiates.
Based on Chinese government reports, it may have up to 15 million drug
consumers, of which 78% are heroine users (Bureau of International
Narcotics and Law Enforcement Affairs [INL] 2009). China being at the
center of the "golden triangle" (i.e., Afghanistan, Laos, and
Myanmar) confirms our earlier point regarding adjacency of production
and consumption locations.
It is difficult to estimate the volume of international trade (or,
depending on the perspective, international trafficking) of narcotics
without hard data on actual consumption quantities and prices.
Nonetheless, since we observe that almost all opium production is in
Afghanistan, and most consumers are in North America, Europe, and
East/Southeast Asia, the volumes of international trade in opiates must
be substantial. Similarly, in the case of cocaine, almost all production
is in South America, with the majority of consumers in North America and
Western Europe, again implying substantial trade.
The fiscal costs of drug enforcement in developing countries can be
quite high, especially in countries that have chosen to address drug
production and trafficking forcefully. (5) Since many major
drug-producing/exporting countries do not have the means to combat drug
production and trafficking, foreign aid plays a vital role in dealing
with the global drug markets. While various U.S. agencies provide
assistance to foreign countries to combat drug production and trade,
most goes through the INL. Table 3 shows the amount of foreign
assistance via INL and the major recipients for 2011 and 2012
(estimated). Afghanistan accounted for 25% (16%) of total INL assistance
in 2011 (2012). The second largest recipient of INL-directed assistance
is Colombia, with a share of 12% (8%) in 2011 (2012). The figures for
Afghanistan include U.S. defense spending in Afghanistan to fight the
Taliban and al Qaeda, groups that have strong ties to drug production
and trafficking.
III. THE MODEL
We now turn to a model to formalize the interactions between drug
trade/trafficking, enforcement, and foreign aid. Assume an open economy
with three production sectors: a licit composite good sector (a net
importable), an illicit narcotics sector (an exportable), and a law
enforcement sector. The country is assumed to be a signatory to the U.S.
anti-narcotics conventions, and given its commitment to those
conventions (and other potential objectives) uses its law enforcement
sector to restrict narcotics production activities. We assume that all
three sectors use labor in their production processes, represented by
the following functions:
(1) N = [F.sub.N]([L.sub.N]),
(2) [pi] = [F.sub.[pi]] ([L.sub.[pi]]),
(3) Y = [F.sub.Y] ([L.sub.Y]),
where N and Y are the production quantities for narcotics and the
composite good, respectively, and [pi] denotes the proportion of people
caught and detained due to engagement in narcotics activities. The
variables [L.sub.N], [L.sub.[pi]], and [L.sub.Y] are labor usages by the
narcotics, law enforcement, and composite good sectors, respectively. We
impose standard assumptions on these production functions, that is,
F' > 0, F" < 0, and constant returns to scale in the
production sectors. Since we interpret [pi], the output of the
enforcement sector, as the rate of incarceration, we also impose
[F.sub.[pi]]([L.sub.[pi]]) [member of] [0,1) for [L.sub.[pi]] [greater
than or equal to] 0. Note that [L.sub.N] is the number of narcotics
workers who have evaded incarceration and who are actively engaged in
narcotics production. Diminishing returns is a consequence of implicit
fixed factors in the production sectors. That is, there are some
resources specifically suited to narcotics production and some suited to
production of the importable. In the enforcement sector, it is
equivalent to assuming that capturing narcotics workers is easy at
first, but becomes increasingly difficult as a greater proportion of
narcotics workers are incarcerated. (6)
Now consider the resource constraints. With full employment of the
available (i.e., not incarcerated) labor resource, we must have
(4) [L.sub.Y] + [L.sub.[pi]] + [L.sub.N]/(1 - [pi]]) = [bar.L]],
where [bar.L] is the fixed stock of labor. In other words, all
labor is employed in one of the three activities, or is incarcerated.
This implies that labor may be idle through incarceration or effectively
idle through being employed in an "unproductive" activity,
narcotics enforcement.
Under competitive markets, the first-order conditions for profit
maximization in the production sectors are given by
(5) [W.sub.N] = P([F.sub.N]([L.sub.N]))[F'.sub.N]([L.sub.N]),
(6) W = [F'.sub.Y] ([L.sub.Y]),
where [W.sub.N] and W are the wage rates in the narcotics and
composite good sectors, and P(x) is the world relative price of
narcotics, which is equal to the producer price in the absence of
effective border measures, and is a function of the export volume. P(x)
is therefore the (inverse) excess demand curve from the world economy,
that is, it is the inverse of D(P) - N(P) where D(P) is the world demand
for narcotics and N(P) is the supply of narcotics from all other
narcotics-producing countries. As noted above, narcotics production is
concentrated, and this is suggestive of market power. Market power for
our economy is defined on the basis of this residual demand. We assume
that P'(x) [less than or equal to] 0, that is, we allow for the
possibility that the economy is "large" with respect to the
narcotics market (in the usual sense, meaning that it faces a downward
sloping residual demand). The "small" country case is where
P'(x) = 0. The importable good is the numeraire. (7)
While workers in the formal sector are paid a competitive market
wage, workers who are employed in the narcotics sector earn a wage
premium to compensate them for the risk of being detained, that is,
[pi]. Therefore, we further maintain that
(7) W = (1 - [pi]]) [W.sub.N].
To interpret this equation, note that 1 - [pi] is the probability
of not being incarcerated. Therefore, the right-hand side of Equation
(7) is the expected wage in the narcotics sector. At equilibrium, this
expected wage must be equal to the wage rate in the composite good
sector. Note also that this implies that the percentage illicit wage
premium is equal to [pi]. This market clearing condition follows Harris
and Todaro (1970). (8)
Finally, we assume that the law enforcement sector is financed by
foreign aid. We therefore have the following financing restriction:
(8) [WL.sub.[pi]] = T,
where T denotes the value of foreign aid to the enforcement sector
in units of the numeraire good. Given that the economy is a recipient of
foreign aid, Equation (8) implies that [L.sub.[pi]] > 0 at
equilibrium. As also implied by Equation (8), law enforcement personnel
are paid the competitive legal wage, hence [L.sub.[pi]] is endogenous,
and all aid reaches the enforcement sector. We are dealing with a case
of tied aid. (9)
Our model is complete with eight endogenous variables and
equations. The endogenous variables are N, [pi], Y, LN, [L.sub.N],
[L.sub.[pi]], W, and [W.sub.N]. These are explained in terms of the
exogenous variables [bar.L] and T, along with the parameters implicit in
the production and excess demand functions. (10) The structure bears
some resemblance to other general equilibrium models of distorted factor
markets, in particular in the use of an expected wage mechanism for
market clearing. The distortions to this market, however, are more
serious and complex than in existing work. In addition to the
incorporation of aid, there are multiple interconnected ways in which
labor can be drawn out of production. In our setup, both incarceration
and enforcement are unproductive activities that are endogenously
determined. Moreover, the wages paid in all sectors are also
endogenously determined, rather than being fixed outside of the model.
IV. THE EFFECTS OF FOREIGN AID
Our first question is how does foreign aid influence a
narcotics-producing/exporting economy? More specifically, how does such
foreign aid affect narcotics and import-competing production, factor
payments, and economic welfare in the recipient nations?
To address these questions we need to explore the comparative
static properties of the general equilibrium system. The core issue in
this model is the allocation of labor across the three activities.
Hence, we begin by substituting Equation (2) into Equation (4), and
Equations (2), (5), and (6) into Equation (7). Finally, substituting
Equation (6) into Equation (8) and then totally differentiating the
resulting expressions with respect to T, we obtain the following system:
(9) [dL.sub.y]/dT + [1 + [L.sub.N][F'.sub.[pi]]/[(1 -
[pi]).sup.2]][dL.sub.[pi]]/dT + 1/[1 - [pi]] [dL.sub.n]/dT = 0,
(10) [L.sub.[pi]] [F".sub.Y] [dL.sub.Y]/dT + W dL.sub.[pi]/dT
= 1,
(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Solving the system of Equations (9)-(11) and simplifying using
Equations (5) and (6) yields:
(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
(14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The terms [[eta].sub.[pi]] =
([dF.sub.[pi]]/[dL.sub.[pi]])([L.sub.[pi]]/[pi]) > 0 and
[[eta].sub.N] = ([dF.sub.N]/[dL.sub.N])(LN/FN) > 0 are the labor
elasticities of output in the law enforcement and narcotics sectors,
respectively, [epsilon] = ([dF.sub.N]/dP)(P/[F.sub.N]) < 0 is the
elasticity of foreign excess demand for narcotics exports from this
economy, and [sigma] = - [F".sub.N]/[F'.sub.N] > 0 measures
the curvature of the production function in the narcotics industry. (11)
It is clear that [OMEGA] < 0 if [[eta].sub.[pi]] [less than or
equal to] (1 - [pi])/[pi], a condition that is satisfied if [pi] (i.e.,
the initial probability of being detained) is sufficiently small. We say
that an economy has an active narcotics sector if the condition holds.
The restriction amounts to a Neary (1978) condition, that is, it
guarantees a normal production/price response in the distorted general
equilibrium. (12) As a practical matter the condition seems to be met in
narcotics-producing economies, so we maintain it throughout the
remainder of the paper. Note also that diminishing marginal productivity
guarantees that [[eta].sub.N] is finite. We can therefore now formally
address the effects of foreign aid on the economic system.
PROPOSITION 1. An increase in foreign aid to restrict narcotics
activities will: (1) Reduce labor participation in and production
(exports) of narcotics and increase anti-narcotics law enforcement
activity; (2) increase the wage paid in the narcotics sector; (3) reduce
the wage paid in the formal sector iff excess international narcotics
demand is sufficiently elastic and narcotics marginal productivity
responsiveness is sufficiently low; and (iv) increase the production of
the import-competing sector under the same conditions.
Part (1) of the proposition is intuitive, and can be seen directly
from Equations (13) and (14), which show that [dL.sub.[pi]]/dT > 0
and [dL.sub.N]/dT < 0 since 0 < [pi] < 1, F' > 0 and
F" < 0 in all production sectors, and P' < 0. However,
our theory elucidates the mechanism. An increase in aid to finance
anti-narcotics law enforcement will lead to an increase in employment in
enforcement at the prevailing wages and therefore to an increase in the
probability of detainment. With workers requiring compensation for the
risk of incarceration, there is an increase in the narcotics premium
above the licit wage. Since labor has moved into enforcement, less labor
is available to other activities. That is, output of either narcotics or
alternative production (or both) must fall. Diminishing returns then
imply that the wage in narcotics and the licit wage in the
import-competing sector cannot both fall at the prevailing prices. Since
the wage premium has risen, however, we must have an increase in the
wage in narcotics, and hence less employment in, and production of,
narcotics.
How does market power matter in terms of the effectiveness of
foreign aid in reducing narcotics production? A "large"
narcotics-exporting economy faces a less elastic foreign excess demand
curve, and in our model the pertinent aspects of the excess demand
function are characterized by e. To the extent that an increase in
foreign aid reduces narcotics production, it has the effect of raising
the world price of narcotics when the recipient is large in world
markets. This price effect works in the opposite direction of the
enforcement effect on narcotics production. (13) This has very important
implications. It suggests that, all other factors constant, foreign aid
will decrease narcotics production and increase enforcement by less the
greater is the market power in narcotics of the recipient economy. In
other words, foreign aid will be more effective at reducing narcotics
production in economies that are small relative to world narcotics
markets than in those that are large, ceteris paribus.
Now consider parts (2) and (3) of the proposition. Increases in
foreign aid will increase the wage in the narcotics sector, as we noted
above, and may increase or decrease the formal wage. From Equation (5)
we have [dW.sub.N]/dT = ([PF".sub.N] +
[F'.sup.2.sub.N]P') ([dL.sub.N]/dT). Hence, establishing that
[dL.sub.N]/dT < 0 and that [dW.sub.N]/dT>0 are one and the same.
Note that there are two effects at work on the narcotics wage. The first
reflects the marginal productivity argument, as labor moves out of
narcotics, the marginal productivity of those remaining increases. The
second is the effect of the terms of trade. As production of narcotics
declines, the price of narcotics rises, increasing the value of workers
remaining in the narcotics industry. The greater the degree of market
power, the larger the latter effect will be for a given decline in
narcotics production. This helps to explain why narcotics production is
less responsive to aid when international demand is less elastic. Aid
increases the probability of detainment, increasing the required wage
premium ceteris paribus, but more of the cost increase can be absorbed
by the export market.
To understand the effect of aid on the licit wage, we turn to the
effect on licit employment, since from Equation (6), dW/dT =
[F".sub.Y] ([dL.sub.Y]/dT). Hence, we can conclude that dWIdT <
0 under the same conditions that [dL.sub.Y]/dT > 0, since these are
the conditions under which labor moves into alternative production, and
we have diminishing marginal productivity. In contrast to Equations (13)
and (14), however, the sign of Equation (12) is ambiguous. Clearly,
[dL.sub.Y]/dT > 0 iff [DELTA] [equivalent to] [PF'.sub.N]
[F'.sub.N] (1 - [pi]) + ([PF".sub.N] + [F'.sup.2.sub.N]
P') (1 - [pi]) [1 + [L.sub.N] [F'.sub.[pi]][(1 - [pi]).sup.2]]
> 0. By slight manipulation, we conclude that Sign ([DELTA]) = Sign
([F'.sub.[pi]]/[[(1 - [pi]).sup.2] + [L.sub.N] [F'.sub.[pi]] +
[[eta].sub.N]/ ([epsilon][L.sub.N]) - [sigma]), where [sigma] is as
defined previously, and [F'.sub.[pi]] [[(1 - [pi]).sup.2] +
[L.sub.N][F'.sub.[pi]] > 0. In turn, it is evident that the sign
of the right-hand side is positive iff [sigma] < [F'.sub.[pi]]
[[(1 - [pi]).sup.2] + [L.sub.N] [F'.sub.N]] + [[eta].sub.N]/
([epsilon][L.sub.N]) = [??]. Hence, the effect of foreign aid on
import-competing production will depend on both the degree of marginal
productivity responsiveness in narcotics, with [??] defining the
critical value, and the degree of market power in the international
narcotics market. (14)
Part (4) of the proposition is less expected, and has significant
policy implications. To explain the intuition behind the effect of
foreign aid on the import-competing sector, assume that the economy is
small and that the conditions of the proposition are met. We have two
opposing forces on the wage premium paid to narcotics workers. On the
one hand, as workers leave narcotics there is a marginal productivity
increase. On the other, there is an increase in the risk of
incarceration, which lowers the expected wage, ceteris paribus. Now, the
lower the value of [sigma], the smaller marginal productivity response
to a reduction in active narcotics workers and therefore the less an
increase in the marginal product can compensate for the increase in
risk. This will motivate more workers to leave the narcotics sector. If
[sigma] is sufficiently low, then more workers will leave the narcotics
sector than the sum of workers moved into the law enforcement sector
plus those being detained. The rest must be absorbed by the
import-competing sector, which therefore expands.
Now reconsider what happens when international demand is very
inelastic. We have already established that in this case narcotics
production, and employment, will not be very responsive to aid. Since
aid finances enforcement directly, this activity must increase, with the
resources being drawn from the import-competing sector. In the limit,
this is the case even if [sigma] is small.
Finally, we note that when the licit wage does decline, an increase
in foreign aid to finance anti-narcotics law enforcement activities will
increase employment in the law enforcement sector by more than the
proportional increase in aid, that is, there will be a magnification
effect. To see this, rewrite Equation (10) as
(15) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where a circumflex denotes a proportional change. The logic is
simply that if conditions are such that the licit wage is pushed down by
the inflow of foreign aid to enforcement, then each unit of said aid
will procure more enforcement workers. But this insight gives us another
useful way of thinking about the consequence of a fall in licit
production. Because the licit wage rises when [dL.sub.Y]/dT<0,
Equation (15) directly implies that an extra unit of aid draws fewer new
workers into enforcement. In essence, when the economy has a lot of
market power and/or when diminishing returns to enforcement kick in fast
enough (i.e., [sigma] is large), some of the aid goes (implicitly) to
increasing the compensation of narcotics workers. In fact, it is even
possible that the wage premium paid to narcotics workers increases in
value terms.
Thus far it has not been necessary to introduce an explicit welfare
index into the analysis, since by design the production and consumption
sides of the model are isolated. It is certainly of interest to evaluate
the welfare implications of policy changes, however, and obtaining a
rudimentary statement on changes in overall economic wellbeing is
straightforward. Let [C.sub.Y] be consumption of the import-competing
good. The national income identity implies that [C.sub.Y] = Y + PN + T,
that is, the value of consumption is equal to the value of production
plus foreign aid. Differentiating totally gives us [dC.sub.Y] = dY + PdN
+ NdP + dT or [dC.sub.Y] = dY + (1 + 1 /[epsilon])PdN + AT. The
left-hand side can be used directly as a welfare measure, in the absence
of externalities. On the right we have three terms: The change in the
value of import-competing output, which we have seen may be negative or
positive in sign, the change in the value of narcotics exports, which
may also be positive or negative depending on whether the terms of trade
effect dominates, and the change in aid, which is positive.
Alternatively, we can write the change in welfare in terms of
changes in factor incomes. Using product exhaustion and Equations (4),
(7), and (8), we can rewrite the welfare expression as [dC.sub.Y] =
[bar.L]dW + [K.sub.N][dr.sub.N] + [K.sub.Y][dr.sub.Y], where [r.sub.N]
and [r.sub.Y] are returns to the narcotics sector and composite
sector-specific factors, [K.sub.N] and [K.sub.Y], respectively. Hence,
on the right-hand side we have the change in the overall wage bill,
where all workers are paid on average W, and the changes in payments to
specific resources. (15)
It is immediately evident that in a world with multiple
distortions, unambiguous welfare conclusions will not be forthcoming.
Nonetheless, we can draw some interesting conclusions from special
cases. Consider a small economy. Despite the absence of terms of trade
effects, aid would be immiserizing if--(dY + PdN) > dT, that is, if a
fall in the value of output from the production sectors more than
offsets the value of the incoming foreign aid. To understand the
conditions under which this might occur, recall that we have established
that dW/dT < 0 only if [sigma] < [??]. Suppose this condition
holds, then we can also conclude that [dr.sub.Y]/dT is positive since
prices are constant. Moreover, [W.sub.N] must rise and [r.sub.N] must
fall as labor is drawn out of the narcotics sector, lowering the value
of the marginal product of this sector's specific factor. All in
all, [dr.sub.N]/dT < 0 reinforces dW/dT < 0 on the right-hand side
of the welfare expression while the rise in [r.sub.Y] will have an
opposing effect. The sum of the negative effects will outweigh the
positive effect if [K.sub.Y] is small. Put differently, immiserizing aid
can occur if the share of payments to capital in the licit production
sector to overall economic activity is low. (16) If, on the other hand,
[sigma] > [??], then [dr.sub.Y]/dT < 0 and dW/dT > 0, while
[dr.sub.N]/dT remains negative. Hence, the possibility of immiserizing
growth is not eliminated, but now can occur if the share of labor in GDP
is low. Thus, we establish a welfare proposition:
PROPOSITION 2. For a small narcotics-producing economy, foreign aid
to anti-narcotics enforcement will lower economic welfare if [sigma]
< [??] and capital is relatively scarce in the import-competing
sector, or if [sigma] > [??] and labor is relatively scarce in the
economy overall.
As the recipient economy being considered becomes larger in the
world narcotics market, the likelihood of immiserization falls, as the
terms of trade effects begin to dominate. That is, foreign aid, by
reducing narcotics production, has the effect of forcing the competitive
narcotics industry to exploit its latent market power. Moreover, if
[sigma] > [??], the larger the initial detention risk, the greater
the welfare loss associated with foreign aid to enforcement. Hence,
somewhat paradoxically, countries that are more successful in their
anti-narcotics activities may be more likely to be harmed in welfare
terms from further foreign aid to their enforcement efforts, ceteris
paribus. The intuition is that the enforcement rate represents the
proportion of workers drawn out of a productive activity, that is, it is
a measure of the degree of distortion. A given shift in economic
activity across a higher distortion generates a greater welfare loss,
ceteris paribus.
V. DEMAND MANAGEMENT AND ALTERNATIVE DEVELOPMENT POLICIES
In addition to providing direct aid for enforcement activities,
from the perspective of narcotics-consuming/importing countries there
are other policy tools that can be employed in order to influence the
production/export of narcotics by the producing countries. Among the
most important is demand management. This refers to a whole range of
policies that result in reduction in the demand in consuming countries,
including educating the public on the negative impacts of drug
consumption, providing drug abuse treatment clinics, and so on. (17) A
reduction in demand will affect the producing countries by depressing
international drug prices, thereby affecting the terms of trade
adversely for the narcotics-exporting country. Equally important as a
policy tool is the development of alternative paths to economic growth
in the producing economy, that is, tailoring additional foreign aid to
encourage alternative production. We can conceive of this as a form of
production subsidy to the non-narcotics-producing sectors, or perhaps as
an investment in the production technology in those sectors.
We consider the implications of a production subsidy first, under
the assumption that the policy is also fully funded by foreign aid.
Since only relative prices matter here, a subsidy to production of the
import-competing good is equivalent to an implicit production tax on
narcotics in this model. (18) Continuing to let P(x) denote the world
relative price of narcotics, the domestic relative producer price of
narcotics can be written P(x)(1 - S), where 0 [less than or equal to] S
< 1 denotes the implicit tax. The relative price for consumers
remains at the world price. We alter Equation (5) such that
(16) [W.sub.N] = P([F.sub.N]([L.sub.N]))(1 - S) [F'.sub.N]
([L.sub.N]).
Setting the initial intervention at zero, substituting Equations
(2), (6), and (16) into Equation (7) and totally differentiating with
respect to S (holding T constant) we obtain
(17)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Solving Equation (17) along with the equivalents of Equations (9)
and (10) as a system and simplifying yields
(18) [dL.sub.Y]/dS = - [WW.sub.N]/[OMEGA],
(19) [dL.sub.[pi]]/dS = [L.sub.[pi]] [W.sub.N]
[F".sub.Y]/[OMEGA],
is, apprehending and incarcerating dealers and users. In the United
States, MacCoun and Reuter (2001) estimate that roughly three-quarters
of national expenditures on drug control are spent on law enforcement,
with treatment and prevention expenditures much less. As Keefer, Loayza,
and Soares (2008) note, evidence on the efficacy of either approach to
demand reduction is limited.
(20) [dL.sub.N]/dS = W/[OMEGA] (W - [L.sub.[pi]] [1 +
[L.sub.N][F'.sub.[pi]]/[(1 - [pi]).sup.2]][F".sup.Y]),
where [OMEGA] is as defined in the preceding section. As is evident
from Equations (18)-(20), [dL.sub.Y]/dS > 0, [dL.sub.[pi]]dS > 0
and dLN/dS < 0. (19) That is, a production subsidy to Y pushes the
domestic relative price of narcotics down (and the world relative price
of narcotics up), resulting in an increase in enforcement and in
alternative production activity. (20) Moreover, in this production model
it does not really matter how the change in the relative price arises.
Hence, we can think of a change in S as representing an exogenous
vertical shift in world narcotics excess demand curve, that is, the
effect of demand management policy.
PROPOSITION 3. A subsidy to import-competing production in the
narcotics-exporting economy or effective demand management programs in
importing economies will result in (1) a reduction in the production of
narcotics; (2) an increase in the production of the import-competing
good; and (3) an increase in the detention rate.
Note that the signs of Equations (18)-(20) do not depend on the
world market power of the economy. However, as [epsilon] [right arrow] 0
from below, all of the expressions approach 0. Hence, a production
subsidy, like financing narcotics enforcement, will tend to be less
effective for economies with a lot of power in the narcotics market.
Now, since dW/dS = [F".sub.Y] ([dL.sub.Y]/dS), it is clear
that the effect on the licit wage, expressed in terms of narcotics, will
be negative due to diminishing returns. For the narcotics wage it is
less clear, since we have [dW.sub.N]/dS = (1 - S) ([PF".sub.N] +
[F'.sup.2.sub.N] P') ([dL.sub.N]/dS) - [PF'.sub.N]. The
first term is positive due to diminishing returns and labor leaving the
narcotics sector. The second term is negative due to the fall in the
domestic narcotics relative price. Rearranging we can show
[dW.sub.N]/dS= (([[eta].sub.N]/([epsilon][L.sub.N]) -
[sigma])([dL.sub.N]/dS) - 1][W.sub.N]. Since the first bracketed term is
less than one, we thereby establish that the second term dominates, and
the wage in the narcotics sector declines.
As for the specific factor rewards, the arguments we made in the
preceding section continue to hold. The specific factor return in the
narcotics sector falls as a result of both a reduction in the relative
producer price of narcotics and outflow of labor from the sector. On the
other hand, the return to the composite sector's specific factor
rises in terms of the numeraire good since labor flows into this sector.
Now suppose that rather than simply subsidizing alternative
production (implicitly taxing narcotics production), investments are
made in the technology of alternative production. In this case, the
effect of alternative development policy is described by modeling an
improvement in production technology in Y. We can rewrite the production
function (3) as Y = [alpha][F.sub.Y]([L.sub.Y]), where [alpha] is a
parameter denoting the level of technology, initialized to unity.
Differentiating the system with respect to a and solving gives us the
effect of a Hicks neutral technological change. (21) The solutions for
the labor allocation across the economic activities can be shown to be
(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(22) [dL.sub.[pi]]/d[alpha] =
[-W.sup.2][L.sub.[pi]]/[OMEGA][L.sub.N]([[eta].sub.N]/[epsilon] =
[sigma][L.sub.N]),
(23) [dL.sub.N]/d[alpha] = [pi]W[W.sub.n]/[OMEGA]([1 - [pi]]/[pi] -
[[eta].sub.[pi]]),
where [OMEGA] is as defined above. Equations (21)-(23), along with
the Neary condition, establish that [dL.sub.Y]/d[alpha] > 0,
[dL.sub.[pi]]/d[alpha] < 0, and [dL.sub.N]/d[alpha] < 0. Hence, we
have the following result.
PROPOSITION 4. Technological improvement in the non-narcotics
sector of the economy will result in (1) a reduction in production of
narcotics; (2) an increase in production of the import-competing good;
and (3) a decrease in the detention rate.
As for the licit wages, there is a marginal product effect which is
negative as labor moves into Y production, and the direct effect of the
improvement in technology. However, the latter dominates. The simplest
way to see this is to use Equation (8) with dT = 0. It is
straightforward to show that dW/d[alpha] = -
(W/[L.sub.[pi]])(d[L.sub.[pi]]/d[alpha]). Since we have established that
d[L.sub.[pi]]d[alpha] < 0, it follows that dW/d[alpha] > 0. For
the narcotics wage we can again simply note that from Equation (5) we
have [dW.sub.N]/d[alpha] = ([PF".sub.N] +
[F'.sup.2.sub.N]P') (d[L.sub.N]/d[alpha]), and since
[dL.sub.N]/d[alpha] < 0, we have [dW.sub.N]/d[alpha] > 0.
Moreover, technology transfer is certainly welfare improving. To
see this, note that with foreign aid to enforcement held constant the
change in welfare is
[dC.sub.y]/d[alpha] = dY/d[alpha] + (1 + 1/[epsilon])p dN/d[alpha].
Using Equations (7), (21), and (23), and the production functions
we can show that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
It follows from our prior assumptions that all of the terms are
positive. Hence, improvement of production technology in the alternative
sector raises welfare in this economic system, in spite of the distorted
environment in which it occurs.
In the case of demand management policies, by contrast, the welfare
effect is ambiguous. The reduction in demand for narcotics in itself
obviously affects welfare negatively. However, here we have an
additional effect as the change in the level of incarceration plays a
role. If the level of incarceration rises, welfare falls as resources
are drawn out of the productive sectors. However, since the rate of
incarceration rises while employment in narcotics falls, the sign of the
change in the level of incarceration is ambiguous. In the case of
subsidizing alternative production financed through a transfer, the
change in welfare would have one additional positive term (i.e., the
value of the transfer) but the overall change remains ambiguous.
Evidently, alternative development policy in the form of technology
transfer has some substantial advantages over merely financing
enforcement, subsidizing alternative production or demand management
from the perspective of the narcotics-producing economy. It achieves the
objective of reducing narcotics production and increasing alternative
production. However, it also reduces the need for enforcement, and
thereby unambiguously frees resources to enter productive activities.
The latter is in contrast to the other policy scenarios, whereby
reductions in narcotics production are always accompanied by increased
enforcement.
Of course, from the donor's perspective, one might be more
interested in the question of which type of policy generates more bang
for the buck, in terms of reductions in narcotics production. The answer
depends on how much it costs to raise productivity in the recipient.
Rearranging Equations (14) and (23) for the same change in narcotics
employment gives us d[alpha] = [THETA]dT where [THETA] = ([W.sub.N]
[F'.sub.[pi]] - [1 + [L.sub.N][F'.sub.[pi]]/[(1 -
[pi]).sup.2]] [F".sub.Y]) / ([W.sup.2] - [pi] [WW.sub.N]
[[eta].sub.[pi]]. In words, [THETA] might be called the productivity
equivalent of an aid dollar. It is the percentage change in overall
productivity in the consumption sector that is equivalent to a one unit
transfer of aid to the enforcement sector, in terms of its effectiveness
in reducing narcotics production. Put differently, [THETA] is the
minimum change in productivity achieved through training, and so forth,
that would make spending one dollar on the training cost effective
relative to spending the same dollar financing enforcement directly.
VI. ROBUSTNESS TO ALTERNATIVE ASSUMPTIONS
We now consider to what extent our results are robust to
alternative characterizations. In particular, we consider what happens
if the enforcement mechanisms changes, and the possibility that the
extent of criminal activity directly affects the likelihood of
successful enforcement.
Consider the enforcement mechanism. At first glance, it may appear
that the results of the preceding sections were driven by the assumption
that workers employed in the narcotics sector are incarcerated when
caught. In some cases this may be impractical or unrealistic (e.g.,
where the costs of incarceration are prohibitive). Accordingly, let us
make an alternative plausible assumption: when the anti-narcotics
law-enforcement personnel find activity in the narcotics sector, they
seize and destroy the narcotics but let the workers go free and return
to the labor force. Now the only source of labor "idleness" is
enforcement.
Assume that factors of production are paid in units of narcotics.
(22) Hence, workers in narcotics are still paid a premium that reflects
the probability of capture. In this case we need to make only two
adjustments to our model of production from Section III. Equation (4) is
modified as follows:
(24) [L.sub.Y] + [L.sub.[pi]] + [L.sub.N] = [bar.L].
This implies that there will be no narcotics workers incarcerated.
Next we need to account for the effect of seizures on international
prices, so Equation (5) becomes:
(25) [W.sub.N] = P ((1 - [pi])[F.sub.N]([L.sub.N]))
[F'.sub.N]([L.sub.N]).
This just states that the price received for illicit sale abroad
will depend on the fraction of output that actually makes it to the
market. The modified model is also a complete system. By differentiating
Equation (24), and substituting Equations (2), (25), and (6) into
Equation (7) and differentiating we obtain
(26) [dL.sub.Y]/dT + [dL.sub.[pi]]/dT + [dL.sub.N]/dT = 0,
(27) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
By solving the new system (26), (27), and (10) for the labor
allocation we find
(28) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
(29) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(30) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Since e < 0 it follows that [PHI] < 0 if [[eta].sub.[pi]]
[less than or equal to] (1 - [pi])/[pi]), as before. Hence, Equation
(29) establishes that an increase in foreign aid to enforcement will
increase employment in enforcement, that is, d[L.sub.[pi]] > 0, as
expected and consistent with modeling enforcement via incarceration.
Now consider narcotics production. Evidently, A[L.sub.N]/AT < 0
provided that the bracketed term in Equation (30) is positive. Given
diminishing marginal productivity this must obtain if [pi] - 1 [greater
than or equal to] [epsilon], that is, if the recipient economy does not
have too much market power. Note also that [pi] - 1 [less than or equal
to] [epsilon] is a sufficient condition to ensure that d[L.sub.Y]/AT
< 0. More generally, however, the sign on A[L.sub.Y]/AT is ambiguous.
PROPOSITION 5. With a seize and release policy, an increase in
foreign aid to anti-narcotics enforcement will result in: (1) an
increase in anti-narcotics law enforcement activities; (2) a reduction
in the production of narcotics if [epsilon] [less than or equal to] [pi]
- 1; and (3) a reduction in the production of import-competing output if
[epsilon] [greater than or equal to] [pi] - 1.
If [epsilon] [greater than or equal to] - 1, we have some
intriguing possibilities. Consider a case where the international excess
demand for narcotics is sufficiently inelastic. Then a seize and release
policy raises the somewhat paradoxical possibility that increasing
foreign aid to enforcement could actually increase narcotics production.
While under the incarceration specification more market power does lead
to a smaller decline in narcotics production as a result of foreign aid
to enforcement (i.e., it limits the policy's effectiveness), under
seize and release the effect of market power is stronger. The intuition
for this paradox is that as more narcotics production is seized, the
world price is driven up. Again, the policy has the effect of forcing
the narcotics industry to exploit its latent market power. With labor
not being incarcerated, the consequent increase in labor's value to
the narcotics industry could be enough to offset the increased risk to
the worker of having their wages seized. Output of narcotics would then
rise, although exports of narcotics, which are net of seizures, must
fall. (23) Unlike some other paradoxical results in the factor market
distortions literature, this one is fully consistent with the stability
conditions outlined in the study by Neary (1978).
Viewed from the perspective of labor movements, with enforcement
drawing in more labor, the licit sector must contract whenever the
illicit sector expands, since no labor can be drawn from a pool of
incarcerated, implying an increase in the licit wage. As noted earlier,
whenever licit production falls, aid is being siphoned into the wages of
narcotics workers. In effect, part of the aid is subsidizing the
narcotics industry.
The ambiguity on economic welfare that we faced in Section IV
remains in this specification of the model. Measuring welfare by
consumption of the import-competing good we have [C.sub.Y] = Y + P(1 -
[pi])N + T, that is, import-competing production plus export production
net of seizures, and the aid transfer. We have seen that the change in
the value of import-competing output may be negative or positive.
Moreover, the change in the value of narcotics exports may also be
positive or negative depending on whether or not the terms of trade
effect dominates. Hence, immiserizing aid remains a possibility. In
addition to the direct effect of a transfer, aid will have positive
terms of trade effect in this case, but tying the aid to an unproductive
activity (i.e., enforcement) can still adversely affect welfare.
We have assumed throughout our analysis that the probability of
capture depends only on the number law enforcement agents. What if, more
realistically, the probability of capture depends on both the number of
enforcement agents and the resources devoted to criminal activity? In
particular, suppose that the likelihood of being captured decreases with
the number of people engaged in narcotics production (imagine evasion
efforts being produced jointly with narcotics). One tractable way to
model this scenario is by replacing Equation (2) of the model with a
logistic function
(31) [pi] = [[a[L.sub.[pi]]/[L.sub.[pi]] + [L.sub.N]].sup.k],
where 0 < a < 1 and k < 1. This is among a class of
"contest success functions" as outlined by Hirshleifer (1989).
A similar specification is used by Grossman (1991) in a classic paper on
insurrection and suppression, and Garfinkel, Skaperdas, and Syropoulos
(2008) also adopt the approach in their analysis of trade in a contested
resource. The approach has been used in a number of other contexts too,
including lobbying and rent-seeking and political campaigns. A recent
overview of the literature is provided by Jia, Skaperdas, and Vaidya
(2013).
We return to the case of increasing aid to enforcement with
incarceration, so the model is complete with the addition of Equations
(1) and (3)-(8). Once again, the key problem is to determine the
allocation of the labor across the economic activities, and the solution
procedure is the same as in the previous specifications. The effect of
an increment to foreign aid to enforcement on the labor allocation can
be shown to be
(32) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(33) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(34) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Note that it can be shown that the partial elasticity of [pi] with
respect to [L.sub.[pi]], [[eta].sub.[pi]], is equal to
k[L.sub.[pi]]([L.sub.N] + [L.sub.K]), so [[eta].sub.[pi]] < k, and
also that [[eta].sub.[pi]] < (1 - [pi])/[pi] for the logistic
function (31), implying that [[pi][eta].sub.[pi]]/(1 - [pi]) < 1. All
other terms are as defined previously.
The expression A contains two terms. The second is unambiguously
positive since [F".sub.Y] < 0. The second bracketed component in
the first term is negative. The first bracketed term, comprised of three
elasticities and [sigma], may be positive or negative, but will be
negative if the probability of being incarcerated is sufficiently low
and/or if the partial elasticity of enforcement is small. If this
sufficient condition holds, then it follows that [LAMBDA] > 0. Once
again, this is a Neary condition that guarantees normal price-output
responses in the model. It then follows from Equation (34) that
d[L.sub.N]dT>0, that is, employment in and production of narcotics
will fall with an increase in aid to enforcement. From Equation (33) we
can state that [dL.sub.[pi]]/dT > 0, again given the Neary condition
is met.
On the other hand, the sign of [dL.sub.Y]/dT is ambiguous. The
first bracketed term is negative. The second term will be negative or
zero if [absolute value of [[eta].sub.N]/ [epsilon] - [sigma] [L.sub.N]]
[greater than or equal to] 1. Since we have established that
[pi][[eta].sub.[pi]]/(1 - [pi]) < 1, this latter condition guarantees
that the first term is negative. Hence, the condition is sufficient for
[dL.sub.Y]/dT < 0. However, we cannot rule out the possibility that
[dL.sub.Y]/dT>0. The possibility may arise for
[pi][[eta].sub.[pi]]/(1 - [pi]) < [absolute value of
[[eta].sub.N]/[epsilon] - [sigma][L.sub.N]] < 1.
In terms of the effect on wages, it is clear that [dW.sub.N]/dT
> 0, since labor leaves narcotics production, which increases the
marginal value of the last worker and, potentially also increases the
narcotics price (for an economy with market power). On the other hand,
the sign of dW/dT is ambiguous, and depends on whether workers leave or
enter alternative production in the aggregate.
The key difference between this specification and the one we
adopted in previous sections lies in the partial effect of a change in
narcotics employment, holding all other labor allocations constant, on
the expected narcotics wage. In the preceding iterations, this was
unambiguously negative, as in standard general equilibrium models. In
this specification, we have the additional complication that the
probability of incarceration falls directly as the narcotics employment
rises, ceteris paribus, and this works in the opposite direction on the
expected narcotics wage. Hence, the Neary conditions that we are
discussing for this particular form of distortion amount to conditions
under which the partial effect on the expected narcotics wage of an
increase in narcotics employment takes the expected (negative) sign.
Clearly, our overall results retain much the same flavor as those
presented in Section IV, in that for stable equilibria an increase in
aid to enforcement will tend to increase enforcement, decrease narcotics
activity and have an ambiguous effect on other production activities,
and the results depend on the magnitude of [sigma] and [epsilon], along
with the partial elasticities in production. Hence, once again, our
production results are robust to reasonable variations of the model
structure.
Finally, we briefly reconsider the welfare results. Our model
simplifies reality by assuming narcotics are a pure exportable, but it
is interesting to think about how the welfare expressions would change
if we allowed for domestic consumption of narcotics. In this case the
income/consumption identity would imply [dC.sub.Y] + Pd[C.sub.N] = dT +
PdN + (N - [C.sub.N])dP + dT, where [C.sub.N] is narcotics consumption.
The left-hand side is again a measure of welfare (the equivalent
variation). The first term on the right may be positive or negative, the
second is negative, the third is positive, and the fourth is positive.
Evidently, the fundamental ambiguity in welfare remains, as does the
possibility of immiserization. To make more definitive statements we
have to impose stronger conditions. Again considering the small economy
case as an example, it can be readily shown that [dC.sub.Y] +
Pd[C.sub.N] = [bar.L]dW + [K.sub.N][dr.sub.N] + [K.sub.Y][dr.sub.Y], and
that all terms on the right take the same signs as argued above. That
is, including consumption of narcotics would not alter Proposition 2 if
the effect on narcotics consumers is considered as a part of welfare. If
we interpret welfare as a government objective function that considers
only changes in licit consumption, then Pd[C.sub.N] must be subtracted
from the change in factor incomes, and the likelihood of immiserization
is reduced.
Of course, in the small economy case, as with the pure exportable
case, any number of characterizations of economic welfare is consistent
with the underlying model. The presence of externalities in consumption
or production, for example, would render using consumption as a proxy
for utility inappropriate. Suppose we think of the public good
"enforcement" as directly generating utility (people feeling
safer on the streets). If we have additive separability, changes in
welfare can be measured as dU = [dC.sub.Y] + h'([pi])d[pi], where
h'([pi]) > 0 is the marginal utility of an increment to
enforcement, measured in units of the numeraire good. Clearly, if the
positive externality is large enough, it may outweigh any shortfall
between the change in the value of output from the production sectors
and the value of the incoming foreign aid, and prevent immiserizing aid.
VII. CONCLUDING COMMENTS
Drug abuse and its attendant problems are long-standing global
challenges, going back at least to the Chinese drug wars of the
nineteenth century. The reach and extent of these problems have,
however, been expanded by rapid globalization due to advances in
communications and transportation. In addition to the economic, social,
and health aspects, narcotics activities have a major global security
dimension.
Therefore, it is important to understand thoroughly the economics
of narcotics markets. While there is an extensive literature explaining
the economics of drug consumption, the literature exploring production
and trade in narcotics is thin. This paper closes some of the gaps, by
drawing attention to the implications of aid and enforcement in
seriously distorted factor markets.
Taking the objective of reducing narcotics production as given, we
explore the impacts of international anti-narcotics policies on the
economies of narcotics-producing/exporting countries. Our approach is to
develop a general equilibrium model of an open economy in which foreign
aid is used to finance law enforcement/anti-narcotics activities. The
key characteristic of the model is that resources can be drawn out of
productive activities by both enforcement and incarceration.
We show that an increase in foreign aid increases detention of
narcotics workers and generally decreases the production of narcotics.
The more market power the economy has, the less effective aid will be in
lowering narcotics production. Our theory also suggests that aid may
lower economic welfare in the recipient economy (even in the limiting
case where it is small and therefore the classical transfer paradox
mechanism is absent) under plausible conditions. Paradoxically, this is
more likely the more successful the recipient has been in its law
enforcement activities. By contrast, technology transfer achieves the
objective of reducing narcotics production while raising economic
welfare, as it reduces the need for enforcement and reallocates
resources toward more productive activities. We also investigate the
implications of whether the enforcement mechanism is based on
incarceration or seizure. Interestingly, we find that under some
conditions an increase in aid to enforcement could actually result in an
increase in narcotics output.
Some of the predictions of our model hinge on the responsiveness of
narcotics output to increases in narcotics employment. While this is
difficult to observe, the lower the degree of responsiveness, the
smaller the implied risk premium to narcotics production. Martin and
Symansky (2006) report gross revenue per hectare in opium production in
Afghanistan of roughly $5,385, compared to roughly $575 for wheat. Opium
production and harvesting is labor intensive, requiring roughly 550
person days per hectare, as compared to 220 for wheat, as reported by
Martin and Symansky (2006).
Nonetheless, assuming similar capital costs, we calculate that
wages in narcotics would be at least triple the wages in wheat
production. Hence, concern over the potential for aid to narcotics
enforcement to be immiserizing may be circumscribed in light of the
small share of capital in economies like Afghanistan, as well as by
their size in world narcotics markets.
Given the sparse theoretical literature in this area, aside from
the direct contribution that our results represent, this theoretical
line of research opens many new avenues in the literature on the
economics of narcotics production and trade. Our approach in this paper
focuses attention on the economic implications of the multiplicity of
distortions introduced into factors markets by narcotics production and
enforcement. The model is of course stylized, and it would be useful to
explore alternative production/factor market structures (Jones and
Coelho 1985; Jones, Coelho, and Easton 1986). There are many other
potentially important extensions to this work. We have considered how
the market power of the aid recipient impacts the effectiveness of aid
in reducing narcotics production, holding other factors constant. A
critical policy question for donors is where aid should be distributed
in order to have the maximum impact on global narcotics production. For
example, in a world with multiple possible aid recipients, we might
specify a dominant supplier and a fringe, and have the donor face an
allocation of aid problem. Future work might also usefully explore other
enforcement mechanisms and policy responses, and perhaps address the
question of "optimal" policies along the lines of Garoupa
(1997). The latter is particularly challenging, and would (at the least)
require a complete characterization of the externalities. Other
interesting extensions might be to model enforcement as a risky
activity, to introduce trafficking agents explicitly, to consider
strategic behavior of various agents, and to explicitly model the
government's behavior with respect to resource allocation (i.e.,
via tax policy and partial financing of enforcement). As an example, it
is possible that increases in enforcement could motivate narcotics
producers to invest in technological improvements in production and/or
evasion.
ABBREVIATIONS
GDP: Gross Domestic Product
INL: Bureau of International Narcotics and Law Enforcement Affairs
UNODC: United Nations Office on Drugs and Crime
doi: 10.1111/ecin.12183
Online Early publication December 18, 2014
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REZA OLADI and JOHN GILBERT *
* We would like to thank the referees for their valuable comments
and suggestions.
Oladi: Department of Applied Economics, Utah State University,
Logan, UT 84322-3530. Phone 435-797-8196,
Fax 435-797-2701, E-mail reza.oladi@usu.edu
Gilbert: Department of Economics and Finance, Jon M. Huntsman
School of Business, Utah State University, Logan, UT 84322-3565. Phone
435-797-2314, Fax 435-797-2701, E-mail jgilbert@usu.edu
(1.) Estimates of the production loss in the United States alone
from incarcerated drug offenders are in the range of $40 billion,
according to the Office of National Drug Control Policy (2004).
(2.) In spite of a heavily financed "war on drugs" led by
the United States, United Nations Office on Drugs and Crime (UNODC)
(2012) estimates that the number of people who used cocaine,
opiates/opioids, cannabis, and amphetamine-type stimulatives in the
world stood at 19.5, 40.5, 224.5, and 52.5 million, respectively, in
2010.
(3.) There are frameworks that provide for such cooperation. The
Single Convention on Narcotic Drugs treaty was signed in 1961. This
treaty and its follow-ups (i.e., the 1971 Convention on Psychotropic
Substances and the 1988 United Nations Convention Against Illicit
Traffic in Narcotic Drugs and Psychotropic Substances) were efforts to
prohibit the production of drugs. These conventions delegated to the
UNODC the tasks of monitoring compliance and working with national
authorities to help them comply with the treaties.
(4.) An existing body of work has considered consumption behavior
(Becker and Murphy 1988; Becker, Grossman, and Murphy 1991; Orphanides
and Zervos 1995), arguments for and against legalization (Becker,
Grossman, and Murphy 1991; Miron and Zwiebel 1995; Miron 2003; Keefer,
Loayza, and Soares 2008), law enforcement activities and interdiction
(Benson, Rasmussen, and Sollars 1995; Flower 1996), and the political
economy of enforcement (Thoumi 2005). Clemens (2008) has attempted to
estimate supply responses to policy, while Clemens (2013a, 2013b) show
that anti-narcotics efforts have actually increased resources flowing to
the Taliban in Afghanistan. Most closely related to our paper,
Richardson (1992) showed that legalization coupled with trade
restrictions that improve welfare and leave drug consumption no more
than the amount under prohibition cannot be achieved.
(5.) Keefer, Loayza, and Soares (2008) cite estimates of 6% of
gross domestic product (GDP) in Colombia in 2006, although this includes
expenditures on combating a drug-financed insurgency.
(6.) Note that we begin our analysis with a simple treatment of
enforcement, with the probability of capture depending only on the
number of law enforcement agents. In Section VI of the paper we relax
this assumption by introducing a contest success function specification,
with similar results.
(7.) Note that our specification implies that narcotics are a pure
exportable. This has the effect of separating the production and
consumption sides of the model, which makes the problem analytically
easier to deal with, and allows us to focus our analysis on the
distortions that narcotics production and enforcement introduce to
factor markets, which are the key features of interest.
(8.) For a more recent take on the Harris-Todaro structure see
Oladi and Gilbert (2011). Specifying the wage differential in this
manner implies that workers are risk neutral, and that the disutility
from incarceration itself is zero (i.e., the cost to the worker of
incarceration is only the income foregone).
(9.) Of course, in all such cases, money is fungible, so in reality
only a fraction of aid might reach enforcement. If the fraction is
exogenous, none of the results would change. Otherwise, one could
formulate the model following the corruption literature.
(10.) With wages endogenously determined, the model is fully
simultaneous. One can also consider a closure where the licit wage is
fixed in terms of the numeraire and labor market slackness results. In
this case the structure of the model is recursive. It can easily be
shown that Equations (6) and (8) would give us [L.sub.Y] and
[L.sub.[pi]], Equations (2) and (3) [pi] and Y, Equation (7) [W.sub.N],
Equation (5) [L.sub.N], and finally Equation (4) economy-wide
employment. The effect of aid is then direct.
(11.) By definition, the elasticity of demand along the excess
(residual) demand curve faced by the economy is [epsilon] =
[[epsilon].sub.D](D/(D - N)- [[xi].sub.N](N/(D - N)), where
[[epsilon].sub.D] is the elasticity world demand for narcotics, and
[[xi].sub.N] is the elasticity supply of narcotics from other countries,
that is, it is a linear combination of the world market elasticities.
The expression c is reminiscent of the Arrow-Pratt index of risk
aversion, and can be thought of as a measure of how rapidly diminishing
returns hits in the narcotics industry.
(12.) Note that both sides of the condition are endogenous, and
that as it increases, resulting in a reduction of the right-hand side,
[pi] may increase or decrease, but is bounded between 0 and 1. Clearly,
if [pi] < 0.5, the condition holds irrespective of the shape of
[F.sub.[pi]]. More generally, the condition holds for larger it the
greater the curvature of [F.sub.[pi]], that is, the greater is
-[F".sub.[pi]]/F'.sub.[[pi]. That is, the faster it becomes
difficult to capture narcotics workers, the greater the threshold level
of enforcement. While the exact form of the condition varies with the
nature of the distortion, a Neary condition is common to all general
equilibrium models with factor market distortions, such as the Harris
and Todaro (1970) model. We restrict our analysis to equilibria that are
guaranteed stable.
(13.) In fact, in the limit, as [epsilon] [right arrow] 0 from
below, [dL.sub.N]/dT [right arrow] 0, while [dL.sub.[pi]]/dT [right
arrow] (W - [1 + [L.sub.N][F'.sub.[pi]]/[(1 - [pi]).sup.2])
[[L.sub.[pi]] [F".sub.Y]).sup.-1] We do not suggest that facing an
excess demand elasticity of zero is likely. Nevertheless, the thought
experiment is useful for understanding the properties of the model, and
the distinction between "large" and "small"
narcotics-producing economies, as previously defined.
(14.) If the economy in question is "small" with respect
to world narcotics market, the second term in the condition drops out.
On the other hand, as the international demand becomes less elastic for
a given [sigma], the condition becomes less likely to hold, and indeed
cannot hold in the limit as [epsilon] [right arrow] 0, implying that
import competing output must fall in this case.
(15.) Wage income in the economy is W([L.sub.Y] + [L.sub.[pi]]) +
[W.sub.N][L.sub.N]. Note that [L.sub.N]/(1 - [pi]) = [L.sub.N] + I where
I is the number of incarcerated narcotics workers. Evidently,
W([L.sub.N] + I) = [L.sub.N]W/(1 - [pi]) and W/(1 - [pi]) = [W.sub.N].
That is, a worker in the narcotics sector is paid, on average, W. The
wage premium accounts for those unpaid while incarcerated. Hence the
wage income is W[bar.L].
(16.) Based on figures from Martin and Symansky (2006), we estimate
that the relevant share in Afghanistan in 2005 was approximately 20%.
(17.) Demand management may also include "direct" market
reduction measures in the developed economies, that
(18.) We recognize that an explicit production tax on the narcotics
sector is difficult to implement, as it is illicit. However, our
approach is purely for consistency with our numeraire choice.
(19.) The significance of the requirement for that [[eta].sub.[pi]]
[less than or equal to] (1 - [pi])/[pi], as highlighted in the preceding
section, should be immediately clear from Equations (19) and (20). It is
required for normal price/output responses as stated.
(20.) Note that our model precludes the possibility of Metzler
(1949)-type paradoxes as the marginal propensity to import/export is
one.
(21.) The implicit assumption is that productivity can be improved
in the alternative production sector without directly affecting
narcotics production. Some types of technology transfer might have the
potential to change productivity narcotics also, for example,
improvements in licit cultivation techniques.
(22.) The former assumption is made simply for convenience, but is
in fact not unrealistic. As Keefer, Loayza, and Soares 2008 note, it is
common for drug traffickers to pay local collaborators in kind.
(23.) To see this, note that dX/dT, where X = (1 - [pi])[F.sub.N]
is the volume of exports, is monotonically increasing in - i/[epsilon],
and approaches zero as - 1/[epsilon] approaches infinity.
TABLE 1
Drug Cultivation (000 ha) and Production (Metric Tons)
Opium (2010) Cocaine (2008)
Countries Cultivation Production Cultivation Production
Afghanistan 123.0 3,600.0
Bolivia 31.0 113.0
Colombia --(a) 62.0 450.0
Laos 3.0 18.0
Mexico 14.0
Morocco
Myanmar 38.1 580.0
Pakistan 1.7 43.0
Peru 61.0 302.0
Total 190.7 4,700.0 167.6 865.0
Cannabis (2010)
Countries Cultivation Production
Afghanistan 9.0-24.0 1,200.0-3,700.0
Bolivia
Colombia
Laos
Mexico 16.5
Morocco 47.0 38,760.0
Myanmar
Pakistan
Peru
Total
Note: Empty cells indicate that data are not available.
(a) Less than 1,000 hectares.
Source: UNODC (2012).
TABLE 2
Estimated Number of Drug Consumers (Millions) and Prevalence
Rate (%) in 2010
Opiates
Percentage
Number of of World Prevalence
Countries Consumers Consumption Rate
Eastern Africa 0.54 3.2 0.4
Northern Africa 0.33 2.0 0.3
Southern Africa 0.28 1.7 0.3
West and Central Africa 0.95 5.7 0.4
Africa 2.11 12.6 0.4
Caribbean 0.80 4.8 0.3
Central America 0.20 1.2 0.1
North America 1.31 7.8 0.4
South America 0.11 0.7 0.04
Americas 1.52 9.1 0.2
Central Asia 0.42 2.5 0.8
East/Southeast Asia 4.31 25.7 0.3
Near and Middle East 2.70 16.1 1.0
South Asia 2.70 16.1 0.3
Asia 10.14 60.4 0.4
East/Southeast Europe 1.87 11.1 0.8
West/Central Europe 1.11 6.6 0.3
Europe 2.98 17.7 0.5
Oceania 0.40 2.4 0.2
World 16.79 0.4
Cocaine
Percentage
Number of of World Prevalence
Countries Consumers Consumption Rate
Eastern Africa -- -- --
Northern Africa 0.0 0.3 0.0
Southern Africa 0.6 3.9 0.8
West and Central Africa 1.5 9.4 0.7
Africa 2.8 17.1 0.5
Caribbean 0.2 1.1 0.7
Central America 0.1 0.8 0.5
North America 5.0 30.8 1.6
South America 1.8 11.3 0.7
Americas 7.2 44.1 1.2
Central Asia -- -- --
East/Southeast Asia 0.4 2.6 0.0
Near and Middle East 0.1 0.4 0.0
South Asia -- -- --
Asia 1.3 7.8 0.1
East/Southeast Europe 0.5 3.0 0.2
West/Central Europe 4.2 25.6 1.3
Europe 4.7 28.7 0.8
Oceania 0.4 2.3 1.5
World 16.2 0.4
Cannabis
Percentage
Number of of World Prevalence
Countries Consumers Consumption Rate
Eastern Africa 5.84 3.4 4.2
Northern Africa 7.53 4.4 5.7
Southern Africa 4.33 2.5 5.4
West and Central Africa 27.26 16.0 12.4
Africa 44.96 26.4 7.8
Caribbean 0.76 0.4 2.8
Central America 0.59 0.3 2.4
North America 32.95 19.4 10.8
South America 6.51 3.8 2.5
Americas 40.81 24.0 6.6
Central Asia 2.05 1.2 3.9
East/Southeast Asia 9.71 5.7 0.6
Near and Middle East 8.14 4.8 3.1
South Asia 32.10 18.9 3.6
Asia 52.99 31.2 1.9
East/Southeast Europe 6.15 3.6 2.5
West/Central Europe 22.53 13.2 6.9
Europe 28.68 16.9 5.2
Oceania 2.63 1.5 10.9
World 170.07 3.8
Note:--indicates that data are not available.
Source: UNODC (2012).
TABLE 3
INL Foreign Assistance ($U.S. Millions)
Recipients 2011 (Actual) 2012 (Estimate) (a)
Afghanistan 400.0 324.0
Bolivia 15.0 7.5
Colombia 204.0 160.6
Mexico 117.0 248.5
Pakistan 114.3 116.0
Peru 31.5 29.0
West Bank/Gaza 150.0 100.0
Others 562.0 1,019.2
Total 1,593.8 2,004.7
(a) Figures for Afghanistan and Pakistan include
overseas contingency operations.
Source: Bureau of International Narcotics and Law
Enforcement Affairs (2012).
