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\begin{document}
\title{Debt and poppy cultivation---Driving forces behind Afghan opium
production} \author{Fredrik Willumsen \\
\texttt{fredrihw@student.sv.uio.no}}
\date{Extremely preliminary draft}
% \maketitle
\pagenumbering{roman}
\section*{Preface}
\addcontentsline{toc}{section}{Preface}
\textbf{Supervisor:} Kalle Moene, University of Oslo.
\subsubsection*{Summary}
In this master thesis I intend to study opium production in
Afghanistan, and identify important drivers behind the opium
production. The main aim is to test whether or not Afghan opium
production is debt--induced.
A claim often found in the literature on Afghan opium production is
that the production of opium is debt--induced. In the first part of
the thesis I provide a theoretical rationale for why this is the case,
using a dynamic model of the cropping choice of a utility maximizing
household. The main finding is that optimal effort devoted to opium
production is increasing in the level of debt.
In the second part of the thesis I describe the data set, and put up
correlation tables for opium production and debt. The findings are
consistent with the literature---the conditional probability of
producing opium given debt is significantly higher than the
conditional probability of producing opium given non--negative wealth.
But correlation does not necessarily imply causation. In the third
part of the thesis I therefore estimate reduced form versions of the
theoretical model, calculating the choice probabilities for different
cropping strategies. Here the findings diverge from the
literature---when controlling for price incentives, eradication risk,
social class, and regional--specific fixed effects, the conditional
probability of producing opium is independent of debt.
To explain this finding I, in the final part the thesis, show that
heterogeneity in moral costs may create two subpopulations of opium
farmers. The first, the ``opportunists'', produce opium for the
unrivalled profit, while the second, the ``moralists'', produce opium
out of necessity. Utilizing the theoretical model with moral costs, I
find that the ``moralists'' either will produce opium at maximum
capacity or not at all, while the ``opportunists'' will have a
production level somewhere in between. Taking this into account when
calculating choice probabilities, our model fits the data better: for
the ``moralists'' debt is an important determinant of opium
production, while for the ``opportunists'' debt is unimportant.
\subsubsection*{Acknowledgements}
This master thesis is written as a part of a bigger project on the
underdevelopment of Afghanistan, led by Kalle Moene. I will like to
thank my supervisor Kalle Moene for involving me in this project,
which is a part of his engagement at the Centre for the Study of Civil
War at the Peace Research Institute of Oslo (PRIO).
\newpage
\tableofcontents
\addcontentsline{toc}{section}{Contents}
\newpage
\section{Introduction}
\pagenumbering{arabic} The purpose of this master thesis is to
describe the Afghan opium farmers and examine the incentive structure
the farmers face: what characterize the farmers that choose to produce
opium and what are the main factors that motive the farmers to produce
opium? We are especially interested in the effect of debt on the
choice of cropping strategy.
Why is this an important topic? There is a widespread belief that
anti--drug efforts have to be aligned with the incentives of the
farmers to be successful. Hence, if debt is an important determinant
of opium production, the Afghan government should focus more on
alternative development than eradication efforts. But despite of the
enormous focus on the link between debt and opium production in the
literature there has, to my knowledge, not yet been done a thorough
statistical analysis of the question. Studies in this line of research
are often of a more qualitative nature, more focused on in--depth
interviews than quantitative analysis.
The questions we address are the following:
\begin{itemize}
\item Is opium production debt--induced? And for what parts of the
population is opium production debt--induced?
\item To what income group(s) do the farmers that produce opium
belong?
\item What is the relative importance of price incentives?
\item What is the effect of the government of Afghanistan's
eradication program?
\end{itemize}
The data set used is from a survey conducted by the United Nations,
Office on Drugs and Crime (UNODC). The data set is thoroughly
described in UNODC's report from the survey
\citep{unodc_farmers}. \citet{unodc_farmers} also examine some of the
questions we are interested in, however they mostly analyze and report
simple correlation schemes. We are more interested in doing a more
thorough statistical analysis of the cropping decisions of the Afghan
farmers, going a step beyond reporting correlations. We use discrete
choice methods to analyze what factors are important determinants for
opium production---taking into account that explanatory variables may
be correlated, which can make inference from simple correlations
biased.
The thesis is organized as follows. The first part presents a simple
two--period model for the cropping decision, where the
farmer/household acts as a utility maximizer subject to resource
constraints. The model shows that opium production will be an
increasing function of the level of debt and, provided that the debt
is large enough, initial debt will affect the cropping profile of the
farmer in several consecutive periods. In addition, because of the
salaam debt system, production will be shifted towards production
today relative to production next period if the farmer has debt, while
not if the farmer has positive wealth. To avoid the effect of the
induced stop at time 2, and since opium production obviously is
subject to stochastic disturbances, we expand our model to an infinite
horizon model with uncertainty. The finding here is equal to the
finding in the two--period model, effort devoted to opium production
is increasing in the level of debt. Moral costs related to the
production of opium is also an important determinant of opium
production. When this is introduced into the model we find that
farmers with a high moral cost term will have more discontinuous
shifts in the optimal strategy than other farmers. The farmers with a
high moral cost term will, when their level of debt passes some
individual threshold determined by their moral cost term, supply very
high effort to be able to repay their debts. The effort will be
increasing in the moral cost term.
In the second part of the thesis I describe the data set, and put up
correlation tables for opium production and debt. The findings here
are consistent with the literature---the conditional probability of
producing opium given debt is significantly higher than the
conditional probability of producing opium given non--negative wealth.
In the third part of the thesis I estimate reduced form versions of
the theoretical model, calculating choice probabilities for different
cropping strategies. Here the findings diverge from the
literature---when controlling for price incentives, eradication risk,
social class, and regional--specific fixed effects, we find no
significant effect of debt on the conditional probability of being an
opium producer.
To explain these findings I, in the final part the thesis, show that
heterogeneity in moral costs may create two subpopulations of opium
farmers. The first, the ``opportunists'', maximize profit, while the
second, the ``moralists'', produce opium out of necessity. We also
find that the two groups will have a different cropping strategy,
which makes us able to distinguish them empirically: the ``moralists''
will produce zero opium until their accumulated debt reaches a tipping
point, and when this point is reached they will produce at maximum
capacity. The ``opportunists'' will find it optimal to diversify their
production. Taking this into account when calculating choice
probabilities, our model fits the data better: debt is an important
determinant of opium production for the ``moralists'', while
unimportant for the ``opportunists''.
\bigskip
This thesis is a part of a research project on Afghanistan, led by
Kalle Moene, where we look at opium production as a special case of a
resource curse. It is a \emph{curse} in the sense that production of
opium works as a poverty trap---poverty is the reason why the farmers
produce opium, and at the same time opium production is a hinder for
alternative development and industrialization of the rural parts of
Afghanistan, hence it is also the reason why the farmers are poor. It
is a \emph{resource} curse since the Afghan soil is extremely well
suited for production of opium. We hypothesize that the opium traders
induce opium production by lending money to poor farmers at salaam
terms, terms which imply that the farmers must repay the loan in
kind. To be able to obtain the loan, or at least to be able to repay
it, the farmers will have to produce opium. In this way the traders
have an instrument as moneylenders to control what the farmers
produce, without producing opium it is much harder for farmers to
obtain loans. A strong implication of this general hypothesis is that
farmers that have debt will have a different cropping pattern than
other farmers, and the investigation of whether this is the case or
not is a central part of this thesis.
\bigskip
The thesis draws on a (small) strand of literature focusing on the
factors that drive opium production in Afghanistan. Several authors
have attributed the increase in opium production after 2001 to the
persistent high prices of raw opium (see for example \citet{molla2003}
and \citet{survey2003}), while others point out a more diversified set
of incentives for farmers to increase their production
\citep{mansfield_myth, mansfield2004, mansfield2005,
mansfield_pain2006, unodc_farmers}. \citet{clemens05} estimates a
structural model to test the effect of different policy regimes on
opium production. This master thesis draws especially from
\citet{mansfield2004, mansfield2005} and \citet{strat3}, while doing
more advanced statistical analysis like \citet{clemens05}. However, as
we have micro--level data, we put weight on the moral costs of
production and the effect of debt. \citet{clemens05} uses macro--level
data on opium production, focusing primarily on price incentives,
labor constraints, stigma of opium production and eradication risk.
\newpage
\section{The Afghan opium economy}
Afghanistan is \emph{the} major opium producing country in the
world. Newly released figures for production in 2005, reported in the
World Drug Report 2006 \citep{wdr2006}, show that Afghanistan produces
89 \% of the world's total produced quantity of opium, making the
country the sole supplier of opium to the world market. However, the
World Drug Report 2006 also reports that opium production in
Afghanistan in 2005 has decreased by nearly 20 \% relative to 2004, a
significant decrease which comes after three consecutive years of
growth in both produced quantity and hectares of land devoted to opium
production. As we can infer from this, and from Figure \ref{9005}, the
amount of opium produced and the amount of land devoted to opium
production are not static sizes, they exhibit substantial variation
both over time and over space. This implies that farmers are going in
and out of production of opium, a variation which we also find in our
data set. This variation is important for our analysis, as it gives us
the opportunity to pin down the values of the parameters in our model.
\begin{figure}[ht]
\begin{center}
\includegraphics{wdr2006_chap3_opium.pdf}
\caption{Afghanistan opium poppy cultivation in thousands of
hectares. Source: World Drug Report 2006}\label{9005}
\end{center}
\end{figure}
One question naturally arises: how did Afghanistan end up as the
world's number one narcotic state? While there of course are several
reasons for this, a quick look at recent historical events might prove
valuable.
\citet[page 10]{unodc_opec03} identifies three major causes as to why
the opium economy in Afghanistan developed:
\begin{itemize}
\item lack of effective government administration
\item degradation of agricultural and economic infrastructure
\item a war economy and related black marketeering
\end{itemize}
Afghanistan has been a war site ever since the Soviet invasion in
1979. Due first to the invasion, and later to the political
vacuum that was created after the fall of the Soviet empire and the
withdrawal of the Soviet forces, there has never been a truly
effective government administration in Afghanistan. Not even today,
five years after the US--led invasion in 2001, and with the presence
and support of huge numbers of foreign military troops, the government
can be said to have control with all areas of the country. This lack
of effective government control has given drug traffickers and
other criminals the opportunity to develop an illegal
economy, consisting of trade with arms, drugs and financing of
terrorist activities \citep{unodc_opec03}.
A consequence of the wars and conflicts is that most of the important
agricultural and economic infrastructure has been destroyed. The
destruction of the infrastructure has made opium production even more
attractive, since opium production does not face the same constraints
as other agricultural production. Opium is for example storable, hence
the lack of transportation possibilities and roads is less severe than
if the farmer produced vegetables that had to be sold at a market
right after harvesting. Opium is also less susceptible to lack or
irregularities in the supply of water \citep{bulletin1999}, a
comparative advantage when most of the irrigation systems are
destroyed.
Another consequence of the conflicts is that the financial sector has
ceased to exist, and an informal financial sector has developed
\citep{unodc_opec03}. Two major problems have emerged from
this. First, the number of loans taken up for investments has dropped,
two thirds of the loans taken up are now used for social needs, such
as food and clothing \citep{helmand2000}. Second, the preferred
collateral is opium, which gives extreme incentives to produce opium
\citep{mansfield_myth}. Opium becomes a poverty trap---farmers produce
opium to be able to obtain credit to survive, but since they are
producing opium, and hence are contributing to the informal economy,
investments in economic infrastructure and the formal sector are
crowded out.
Yet another important factor for the emergence of the opium economy
was the Taliban, which can be said have emerged as a response to the
lack of a state apparatus in the beginning of the 1990's. This
movement in fact encouraged opium production, at least from 1997 and
onwards \citep{rashid02}, as they realized that opium production could
fund their own activities. And even though they strictly enforced laws
against other forms of criminal activities (the use of opium was for
example prohibited, and the debarment was extremely efficiently
enforced) the production of opium for use outside Afghanistan was not
considered to be anti--Islamic.
Also several other reasons as to why the narcotic state emerged can be
provided. The crackdown on production of opium in Iran and Pakistan
during the 1970's and the 1980's was important, as it pushed illegal
activities into Afghanistan, where the lack of a state apparatus gave
wide opportunities for opium traders and other criminals. Afghanistan
place on the map is also important; situated in Central Asia, it is
possible to smuggle opium to markets in Asia, Russia, and
Europe. Finally, the Afghan soil is extremely well suited for opium
production. The average yield of opium per hectare land in Afghanistan
is 45 kg, compared to 7 kg/ha in Laos and 11 kg/ha in Myanmar
\citep{unodc_opec03}.
As a tentative conclusion, it is reasonable to believe that
destruction due to war and conflict along with the lack of a
controlling central government, are major explanatory factors behind
the growth of the Afghan opium economy. In the war economy, opium has
become an integral part of the livelihood strategies of many of the
rural communities in Afghanistan \citep{unodc_opec03}.
\subsection{The salaam system}
The salaam system is an informal credit system where the farmer
obtains advances on a fixed amount of future agricultural production
\citep{strat3}. The amount that the farmer receives is often half of
the prevailing market price at the time when the farmer enters into
the salaam arrangement. \citet{strat3}, for example, reports that, in
a sample of 108 farmers from Qandahar and Shinwar, the price received
by the farmers was on average 42 \% of the value of the produced opium
at the harvest time. This factor, labeled $\alpha$ below, is found to
vary over time and space, and it also exhibits a seasonal pattern,
being smaller when close to the harvesting time \citep{strat3}.
While this may seem to be an exploitive credit arrangement favoring
the lenders on behalf of the farmers, the reason that this system
evolved is of a quite different nature. The salaam system arose as a
response to the Islam prohibition of interest on loans, and became
popular in the Taliban period due to the Taliban's very restrictive
interpretation of Islamic laws. The salaam system was introduced as a
mean of providing credit, while not breaking Islam laws. Of course,
since the salaam arrangement gives the farmers only half the value of
the produce relative to harvest time there is a huge implied interest
rate present. However, there is also a risk sharing between lender and
borrower, because they both risk losing due to future price and
harvest variation, and this risk sharing makes the salaam system legal
under Islam; the lender does not take interest per se, he receives a
compensation for taking risk.
Importantly, this is the ideal version of the salaam system. In
Afghanistan today, where credit is needed to get through the winter,
defaulting on a loan is not an option. Defaulting on a loan will imply
that the farmer does not have the possibility of obtaining credit the
next winter season, and hence the farmer will have difficulties
surviving. If the farmer experience a crop failure, there exist two
ways of repaying the loan. The first is to buy opium at the local
bazaar, but if one farmer has experienced a crop failure there is a
high probability that also other farmers in the area have experienced
the same, and hence the supply of opium at the local bazaar may be
non--existent, or opium may be available at a very high price. The
other possibility is to reschedule the debt. The debt will then be
rescheduled at salaam terms, which imply that the farmer will have to
produce twice the amount of opium the next season to be able to repay
the loan (These two alternative repayment strategies are documented in
\citet{mansfield_myth}).
As we can infer from this, the salaam system may lock farmers to opium
production multiple periods after the initial loan was granted. In
addition, as opium is considered to be the preferred collateral
\citep{mansfield_myth}, we a priori should expect to find that debt is
a strong determinant of opium production.
\subsection{Farmers' incentives to produce opium}
In a series of papers, David
\citet{mansfield2004,mansfield2005,mansfield2006} has identified
important driving factors behind Afghan opium
production. \citet{mansfield2004} shows that price incentives alone
are not able to explain the diversity in the cropping pattern in the
2003/2004 season, instead he focuses on food security and access to
land and credit as important determinants of opium
production. Mansfield also found that there was a growing confidence
in the supply of wheat, and this made the farmers substitute
production of wheat for own consumption for opium production. Further,
accumulated debts and the opium--dependent salaam credit system are
considered important determinants. Finally Mansfield finds that the
eradication campaign initiated by the Afghan government has been
counterproductive, the farmers who have experienced eradication
increased the amount of land dedicated to opium production by more
than the farmers who did not experience crop eradication. The
rationale is that when the crops are eradicated, the farmer has to
reschedule his loan, and due to the salaam credit system this will
imply that he will have to produce even more the next season. There is
however no discussion of whether these differences are statistically
significant.
\citet{mansfield2005} finds that there in the 2004/05 season is likely
to be a downturn in the number of households cultivating opium, and he
attributes this to falling farmgate prices, concerns over food
security, and an increased awareness among farmers of the risk of
eradication. However, he still finds that households that experienced
eradication last year, devote more land to opium production than other
farmers.
\citet{mansfield2006} finds that eradication often targets the
poorest, while those that have links to the authorities or have the
financial strength to bribe escape the eradication measures. Again
this will drive up the accumulated debts of the poor, contributing to
increases in opium production.
\bigskip
\citet{unodc_farmers} reports that the two main reasons for farmers
\emph{not} to engage in opium production are that opium is against
Islam and that opium production is illegal. \citet{clemens05}, in a
paper where he estimates the effects of different drug control
policies using a partial equilibrium framework, finds that the stigma
of producing opium is important to be able to account for the observed
prices.
We will draw heavily on these identified drivers in the empirical part
of this thesis.
\newpage
\section{A model of debt--induced opium production}
In this section we show why opium production can be partly
debt--induced, and that optimal opium production will be an increasing
function of the level of debt.
We first model the cropping decision in a simple two--period model
without uncertainty. We then introduce stochastics into the model,
while we at the same time let the time frame go to infinity. Finally
we consider the effect of moral costs on opium production.
The presence of the non--linearity in the budget constraint (equation
(\ref{ibc})), the kink around zero due to the salaam debt system,
makes the problem somewhat less straightforward to solve. The
difficulty that arises, is that there are different cases to consider
depending on the initial wealth $W_0$. The analysis that follows will
therefore be somewhat tedious, as a thorough analysis requires that
the optimal strategies for all the cases are identified. The intuition
is however very simple. The higher the level of debt, the more utility
the household get from producing opium. And given the salaam debt
system, farmers will find it optimal to shift production to the
present period relative to the next if they have debt, while not if
they have positive wealth. For the model with moral costs, the
important intuition is that farmers with a high moral cost term will
have more discontinuous shifts in the optimal opium cropping strategy.
\subsection{Two--period model without uncertainty\label{two-period}}
Let $u(c_t)$ denote a standard utility function, additatively
separable over time, where $c_t$ denotes level of consumption at time
$t$, and the standard conditions $u^{\prime}(c_t)>0$ and $u^{\prime
\prime}(c_t)<0$ holds for all $c_t$. Let $g(x_t)$ denote the cost of
producing $x_t$ worth of opium, where $g^{\prime}(x_t)>0$ and
$g^{\prime \prime}>0$. The household's objective is
\begin{gather}
\max_{\{c_t,x_t\}}\sum_{t=1}^{2} \beta^{t} \left[u(c_t)-g(x_t)\right]\label{J2}
\\
\text{ s.t. }\notag\\
W_{t}=\label{ibc}
\begin{cases}
x_t+W_{t-1}-c_t &\text{ if } x_t+W_{t-1}-c_t \geq 0\\
(x_t+W_{t-1}-c_t)\alpha &\text{ otherwise }
\end{cases}
\\
c_t\geq \bar{c} \: \forall \, t \label{pos_c}\\
W_2 \geq 0\label{end_constr} \\
W_0 \text{ given }\label{init_val}
\end{gather}
The constraints need some explanation. Constraint (\ref{ibc}) is the
intertemporal budget constraint. $W_{t-1}$ denotes wealth inherited
from $t-1$ (possibly negative), $x_t$ the value of the farmer's
production of opium and $c_t$ consumption, all at time $t$. $\alpha>1$
is the salaam parameter. Any debt taken up or rescheduled in period
$t$, denoted $b$, will be transferred into a promise to produce
$\alpha b$ worth of opium in period $t+1$. Anecdotal evidence suggests
that $\alpha \approx 2$ \citep{mansfield_myth}. We here assume that
the individual farmer is not in a position to lend money to other
farmers at salaam terms (the $\alpha$--parameter is only present when
$x_t+W_{t-1}-c_t<0$). Is this a reasonable assumption? We claim so:
since the warlords and commanders are governing the opium industry it
is highly unlikely that a farmer can become a creditor, lending to
other farmers at salaam terms. The warlords and commanders want
control over the production of opium, and they get this control
through controlling the credit system, hence they are unlikely to be
willing to introduce unnecessary competition in the credit market,
deteriorating their own position as the sole provider of
credit. Constraint (\ref{pos_c}) states that consumption must be above
some exogenously given minimum level. Constraint (\ref{end_constr})
states that all debt must be repaid when period 2 is over, and since
the utility function is globally increasing, constraint
(\ref{end_constr}) will hold with equality. Constraint
(\ref{init_val}) says that the initial level of wealth is exogenously
given. We do not model why some farmers are initially rich, while
others are initially poor.
Let $S$ denote the sequence of feasible choices
$((c_1,x_1),(c_2,x_2))$, i.e. the set of sequences that fulfills all
the constraints. We assume that $S$ is not empty, i.e. we assume that
the level of debt at $t=1$ is sustainable. Let us further, for
simplicity, assume that $\beta=1$ and normalize $\bar{c}=0$. We solve
the problem backwards, starting at $t=2$. Let $J(t,W_{t-1})$ denote
the optimal value function at time $t$.
\begin{equation*}
J(2,W_1)=\max_{c_2,x_2} \left\{u(c_2)-g(x_2) \right\} \text{ s.t. }
\begin{cases}
x_2+W_1-c_2=0 \\
c_2 \geq 0
\end{cases}
\end{equation*}
We solve for $c_2$ in the constraint, yielding the unconstrained
optimization problem
\begin{equation*}
J(2,W_1)=\max_{x_2} \left\{u(x_2+W_1)-g(x_2) \right\}
\end{equation*}
First order condition for interior maximum, the intratemporal
optimality condition, is
\begin{equation}
u^{\prime}(x_2+W_1)=g^{\prime}(x_2) \label{intratemp_opt_t=2}
\end{equation}
Assuming an interior optimum exists, $x_2$ can be shown to be a
decreasing function in $W_1$ provided that $u$ is strictly concave and
$g$ is convex. More formally
\begin{proposition}\label{prop_mapping_w2:x2}
Assume that $u^{\prime}(c_t)\vert _{x_t=0}>g^{\prime}(0)$. Then
there exist a function $h: W_1\rightarrow x_2 $ that, provided that
$g$ is increasing and convex, $u$ is increasing and strictly concave
and an interior solution exists in the relevant domain of $W_1$ and
the relevant range of $x_2$, uniquely determines the level of opium
production. The level of opium production will be strictly
decreasing in wealth.
\end{proposition}
\begin{proof}
We prove the statement in Figure \ref{proof_w2}. A positive shift in
$W_1$ shifts the marginal utility curve inwards. The marginal cost
curve is not affected by this shift. As long as the marginal utility
curve is \emph{strictly} concave, the curve will be downward sloping
in $x_2$. And as long as marginal cost curve is convex (note that
strict convexity is not needed), the marginal cost curve will be
horizontal or increasing in $x_2$. It then follows that there always
will be an intersection between the two curves, and, since the
marginal cost curve does not change when $W_1$ change, the mapping
from $W_1$ to $x_2$ will be unique\footnote{Strictness in concavity
is key for the result. Without this property on the utility
function, the marginal utility curve may be horizontal and we may
then not get a (unique) mapping from wealth to opium
production.}. Provided that the marginal utility of producing
opium is greater than the marginal cost at zero production, this
will be sufficient to ensure existence (however, not necessarily
within a reasonable range of $x_t$).
\end{proof}
\begin{figure}[t]
\caption{Proof of Proposition \ref{prop_mapping_w2:x2} $(W_1^{\prime}>W_1)$}
\label{proof_w2}
\centerline{
\beginpicture
\setcoordinatesystem units <65mm,65mm>
\setplotarea x from 0 to 1, y from 0 to 1
\axis bottom /
\axis left /
\put {{$ u^{\prime}/g^{\prime} $}} [b] at 0 1.01
\put {{$ x_2 $}} [l] at 1.01 0
\plot 0.15 0.15 0.85 0.85 /
\put {$ g^{\prime}(x_2) $} [l] at 0.85 0.85
\setquadratic
\plot 0.15 1 0.35 0.55 0.85 0.25 /
\put {$ u^{\prime}(W_1+x_2) $} [l] at 0.85 0.25
\setdashes
\plot 0.15 0.75 0.35 0.40 0.85 0.15 /
\put {$ u^{\prime}(W^{\prime}_1+x_2) $} [l] at 0.85 0.15
\plotheading{\vspace*{3mm}}
\endpicture
}
\end{figure}
$J(2,W_1)$ will be an increasing function in $W_1$: $\partial
{J(2,W_1)}/\partial{W_1}=u^{\prime}(\cdot)>0$ by the envelope
theorem\footnote{$\partial {J(2,W_1)}/\partial
{W_1}=\partial{(u(h(W_1)+W_1)-g(h(W_1)))}/\partial
{W_1}=u^{\prime}(h(W_1)+W_1)(h^{\prime}(W_1)+1)-g^{\prime}(h(W_1))h^{\prime}(W_1)=[u^{\prime}(h(W_1)+W_1)-g^{\prime}(h(W_1))]h^{\prime}(W_1)+u^{\prime}(h(W_1)+W_1)=u^{\prime}(h(W_1)+W_1)>0$
since the first order condition for optimality makes the expression
in the square brackets equal to zero. }. $J(2,W_1)$ will hence be
increasing and concave in $W_1$.
\bigskip
Going to period $t=1$, using the optimal value function for $t=2$, we
get the following maximization problem:
\begin{gather}
J(1,W_0)=\max_{c_1,x_1} \left\{u(c_1)-g(x_1)+J(2,W_1) \right\}\notag\\
\text{ s.t. } \notag \\
W_{1}=
\begin{cases}
x_1+W_0-c_1 &\text{ if } x_1+W_0-c_1 \geq 0\\
(x_1+W_0-c_1)\alpha &\text{ otherwise }
\end{cases}
\label{IBC_t=1}
\\
c_1\geq 0 \notag \\
W_0 \text{ given } \notag
\end{gather}
Due to the non--linear budget constraint, the solution to this problem
will be somewhat involved. The reason is that the behavior of the
farmer will be different for small values of wealth relative to small
values of debt. For small values of wealth the consumption and
production will be equal in the two periods, as wealth can be
transferred without loss between the periods. Equal production and
consumption in the two periods will be optimal since utility is
concave. Small values of debt however, cannot be transferred without
loss between periods, the reason being the salaam debt system
increases the amount of debt with a factor of $\alpha$ if it is rolled
over to the next period. For small values of debt it will hence be
optimal to repay the entire debt now rather than to transfer it to
next period and paying the salaam cost. Consumption and production
will here not be equal in the two periods. A third case arises if the
initial debt is large. For this level of debt it will no longer be
optimal/possible to pay back the entire debt in one period. The reason
is the extremely low consumption and the extremely high production
level that is implied by choosing this strategy. It will hence be
better to pay the salaam cost of borrowing, than to reduce consumption
in the first period that much. There will then exist a level of debt
for which the optimal strategy of the farmer switches from repaying
everything in one period, to paying the salaam cost of borrowing. I
label this level of debt $W^{\ast}$, the \emph{salaam threshold}.
The solution to the problem is characterized in Proposition
\ref{prop_t=1}: \renewcommand{\theenumi}{\Alph{enumi}}
\begin{proposition}
\label{prop_t=1}
Assume that $J(2,W_1)$ is the optimal solution to the problem at
$t=2$, as identified in Proposition \ref{prop_mapping_w2:x2}. Then
there will be three different solutions to the problem at $t=1$,
depending on initial wealth $W_0$:
\begin{enumerate}
\item \label{case1} $W_0\geq 0,W_0+x_1-c_1 \geq 0$. The free
optimization problem. Half of the initial wealth will be spend in
each period; consumption and production will be equal in each period.
\item \label{case2} $W_0< 0,W_0+x_1-c_1<0$. Debt is rolled over from
$t=1$ to $t=2$, $W_0x_{L}$. Expected
production is then
\begin{equation*}
Ex=ex_{H}+\left( 1-e\right) x_{L}
\end{equation*}
where $e$ is effort, $0\leq e\leq 1$. We here assume that the
probability of the good outcome is equal to the effort. This we can do
without loss of generality, as long as the probability of the good
outcome is an increasing and concave function of effort, our results
still follow.
Higher effort implies higher production. The cost of effort is $g(e)$
where $g^{\prime }\left( \cdot \right) >0 $, \ $g^{\prime \prime
}\left(\cdot\right) >0$ and $g^{\prime }(1)=\infty $. In addition we
assume that $\P u(\bar{c})=\infty$, to avoid solutions involving
consumption at or below the minimum level. Finally we assume that
consumption (and hence saving) is chosen ex post, while the production
is decided upon ex ante.
We also need a no--Ponzi game condition, to avoid that the farmer roll
over the debt infinitely. The no--Ponzi game condition will here be
very simple, $W_t\geq x_{\text{max}}\, \forall \, t$, i.e. the debt
have to be below some exogenous given maximum level.
Let the intertemporal budget constraint be given by
\begin{equation*}
W_t=k\cdot (x_t+c_t-W_{t-1})
\end{equation*}
and
\begin{equation*}
k=
\begin{cases}
1 & \text{ if } x_t+c_t-W_{t-1} \geq 0 \\
\alpha & \text{ if } x_t+c_t-W_{t-1} < 0
\end{cases}
\end{equation*}
Let $W_{0}$ be initial wealth. The Bellman equation will then be
\begin{align}
V(W_{t-1})&=\max_{c_t,e_t}\{u(c_t)-g(e_t)+E_tV(W_t)\} \notag\\
&=\max\{u(c_t)-g(e_t)+E_tV[k(W_{t-1}+x-c_t)]\} \notag \\
&=\max\{u(c_t)-g(e_t)+e_tV[k(W_{t-1}+x_H-c_t)]+(1-e_t)V[k(W_{t-1}+x_L-c_t)]\} \notag
\end{align}
Consumption is chosen ex post, while effort is decided upon ex
ante. If $x_t^H$ is realized, consumption is given by
\begin{equation}
u'(c_t^H)=V'\left(W_{t-1}+x_H-c_t^H\right) \label{infty_FOC_consumption_H}
\end{equation}
I assume that $W_{t-1}+x_H-c_t^H \geq 0$ if the good state is
realized. If the bad state $x_L$ is realized, we will again have to
consider cases, depending the level of the start--of--period debt. The
cases will be approximately the same as the ones we identified in the
previous section, hence I use the same labels.
\begin{description}
\item[~\ref{case1}]If $\P u(c_t)=\P V(W_{t-1}+x_L-c_t^L)$ has a
solution where $W_{t-1}+x_L-c_t^L \geq 0$, this level of consumption
will be chosen.
\item[~\ref{case2}] If $W_{t-1}Q(W_{t-1})$, i.e. if the farmer is non--religious, or
if he does not care about the possible social stigma from producing
opium, he would choose to act according to the optimal scheme
characterized in section \ref{infinite_horizon}. But if there are
moral costs to production of opium, a ``fixed cost'' from switching
from other agricultural production to opium, this choice will not be
that obvious. Denote these moral costs by $m_i$, where $i$ indicates
an individual farmer. The farmer's choice of cropping strategy will
then be to choose opium production if and only if
\begin{equation}
V(W_{t-1})-m_i>Q(W_{t-1}) \label{threshold}
\end{equation}
Hence there will, for a farmer with a given moral cost term $m_i$,
exist a threshold for debt for which the farmer switch from other
agricultural production to opium production. But when this choice
first is made, the moral cost term will disappear from consideration,
and we will be back in the case discussed in section
\ref{infinite_horizon} where optimal effort is chosen as a function of
inherited wealth. Why? Because if opium is chosen as a part of the
farmer's cropping strategy, the fixed costs will have turned to sunk
costs, as the moral stigma that is induced by opium production is not
linked to the amount of opium produced. Hence for a farmer with a high
moral cost term, when he first starts to produce opium he is likely to
produce a lot, possibly utilizing all his available resources to opium
production. The farmer may have accumulated debt over several years,
and then finally, when the level of debt passes the crucial threshold
in (\ref{threshold}), the farmer changes strategy from other
agricultural production to opium production. For these farmers we say
that opium production is debt--induced.
I will make the last argument more clear using an example. The
intuition behind the example is the following: the farmers that have a
high moral cost term, we label them the ``moralists'', will for a
sufficiently high level of debt start to produce opium. But, counter
to the farmers that produce opium for profit, whom we label the
``opportunists'', the moralists will when first started to produce
opium, produce at a much higher level. Their opium production can
hence be said to be truly debt--induced, and they will have the
characteristic that they produce closer to maximum capacity.
The example is the following. Assume that the farmer starts out with
$W_{t-1}=0$ and that the farmer has a consumption level of $c$. His
expected pay--off will be $u(c)+Q(0)$ if no shock is to occur
(remember that we for simplicity have set the discount factor to
unity). Let us introduce some furter assumptions. First we restrict
the values that the moral cost term can take, $m_i \in \{m_L,m_H\}$,
where $m_L
\setplotarea x from 0 to 1, y from -0.2 to 1
\axis bottom shiftedto y=0 /
\axis left /
\put {$S(\varepsilon) / m_i$} [b] at 0 1.01
\put {$ \varepsilon $} [l] at 1.01 0
\plot 0 0.75 0.8 -0.1 /
\put {$S(\varepsilon)$} [l] at 0.8 -0.1
\put {$\varepsilon^{H}$} [f] at 0.24 -0.06
\put {$\varepsilon^{L}$} [f] at 0.7 -0.06
\put {$m^H$} [b] at -0.06 0.5
\put {$m^L$} [b] at -0.06 0
\setdashes
\plot 0 0.5 0.24 0.5 /
\plot 0.24 0.5 0.24 0 /
\plotheading{\vspace*{3mm}}
\endpicture
}
\end{figure}
Figure \ref{proof_moral_vs_opportunists} shows that the moralists need
a much worse shock before they start to produce opium than the
opportunists, i.e. before the inequality in (\ref{opium_switcher})
will be fulfilled (here $m^L$ is set to 0). A fraction
$F(\varepsilon^L)$ of the opportunists will produce opium, while only
a fraction $F(\varepsilon^H)$ of the moralists chooses opium, where
$F$ is the cumulative density function of the shock
$\varepsilon$. This means that the average production of the moralists
will be much higher than the average production of the
opportunists. Why? As shown in sections
\ref{two-period}--\ref{infinite_horizon}, opium production will be
increasing in debt (here $c-\varepsilon c$). And since the moralists,
on average, start to produce opium when they are worse off than the
opportunists, they will have higher production levels than the
opportunists.
The model with moral costs, and especially this last example, will be
utilized in section \ref{emp_strat}, where the empiricial strategy is
introduced.
\newpage
\section{Description of the data\label{description_data}}
The data set we use is obtained from United Nations, Office on Drugs
and Crime (UNODC), and it is thoroughly described in
\citet{unodc_farmers}. In this section we will first comment on the
methods used when collecting the data, then describe the most
important variables for our analysis, and finally give some descriptive
statistics and cross--tabulation of these variables. The empirical analysis is
postponed to the next part of the thesis.
The data was collect by UNODC in October 2003, using local
surveyors. The sampling frame was 13,980 villages (out of 30,706 known
villages in the AIMS database), and their sampling strategy was to
sample $2.5 \%$ of the sampling frame, i.e. 347 villages. However, due to
security reasons, several districts in the parts of the Southern
region could not be surveyed, and the UNODC ended up with collecting
data from 308 villages.
An obvious problem with the data is that the sampling frame is
\emph{not} the entire Afghanistan; the UNODC have sampled farmers from
provinces previously known to be producers of opium. Hence, any
conclusion we can draw from our analysis cannot be said to be valid
for entire Afghanistan, we must limit ourselves to give statements
that (hopefully) are valid for the provinces where the sample is drawn
from. In addition, the UNODC questions the method used to sample
individual farmers from the randomly selected villages:
\begin{quote}
``The debriefing sessions [...] revealed
two shortcomings in the random selection process that could lead to
an over--representation of the opium growing farmers in the sample:
the first one is that in some villages the surveyors were directed
by the headmen to interview farmers who were known in the village to
have some experience in poppy growing. The second one is that in
some cases, the surveyors, once in a village, were looking for
farmers working in the fields. In many parts of eastern and southern
Afghanistan, October was the time when farmers were preparing their
fields for sowing opium poppy later in
November.'' \citep[page 50]{unodc_farmers}
\end{quote}
Hence, given the sampling strategy and the shortcomings in the methods
used for sampling of individual farmers, we will have to refrain from
making claims involving aggregation based on the information found in
this data set. However, as we are more interested in the motivation of
the farmers rather than to make aggregate predictions, these
shortcomings in the sampling strategy will not be of major importance
for us. As long as the sampled farmers that are producing opium are
representative for the population of opium producing farmers (and the
non--opium producing farmers are representative for the population of
non--opium producing farmers), our estimates will remain unbiased. We
have no reason to doubt that this is the case.
The data set consists of two parts: one part where 922 farmers are
randomly selected from 308 villages in opium producing provinces, and
another part consisting of interviews with the heads of the same 308
villages. It has proved difficult to get hold of the questionnaire for
the survey, however, it has been possible to infer what the questions
are likely to have been from the data file. The two parts of the data
set have been merged and collapsed so that it is fit for quantitative
analysis using Stata.
\bigskip
Important descriptive statistics are given in Table
\ref{descriptive_stat}\footnote{The amount of opium producing farmers
is different from what \citet{unodc_farmers}
reports. \citet{unodc_farmers} may have added information to the
data set that is not publicly available, but as we do not have this
information, we use the data set as it is provided to us by the
UNODC.}. We see that there is a huge increase in the number of
farmers producing opium in 2004 relative to 2003. It is important to
note that the survey was conducted in October 2003, so the figures for
2004 are the farmer's cropping \emph{intentions} for 2004, hence they
do not necessarily correspond with the actual outcome. Farmers may
have had an incentive to report too high figures of opium production
in 2004 to try to get attention and support from the government and
local authorities. However, as the increase in production from 2003 to
2004 in the whole Afghanistan ex post has proven to be considerable
(see Figure \ref{9005} for the increase in hectares of land devoted to
opium production), we do not consider this to be a serious threat to
the validity of our study.
\begin{table}[ht]
\caption{Descriptive statistics}
\label{descriptive_stat}\centering
\begin{tabular}{lrr}
\hline
& \% of farmers & Observations \\ \hline
Opium 2003 & .76 & 922 \\
Opium 2004 & .87 & 922 \\
Monocrop opium 2003 & .09 & 922 \\
Monocrop opium 2004 & .18 & 922 \\
Start before 2001$^{\ast}$ & .63 & 804 \\
Start 2002$^{\ast}$ & .10 & 804 \\
Start 2003$^{\ast}$ & .19 & 804 \\
Start 2004$^{\ast}$ & .08 & 804 \\ \hline
\end{tabular}
\begin{tabular}{l}
$^{\ast}$ \% of farmers producing opium in 2004%
\end{tabular}%
\end{table}
In table \ref{cross_tab:debt_opium03} and table
\ref{cross_tab:debt_opium04} we report cross--tabulations of opium
producers and debt (relative figures are given in parentheses). Debt
is here a dummy variable taking the value of 1 if the farmer has taken
up debt prior to 2003/in 2003 and 0 otherwise. Opium producer is also
a dummy variable taking the value of 1 if the farmer is an opium
producer and 0 otherwise. We restrict the sample to include only those
respondents who are farmers in 2003 and 2004 respectively. In table
\ref{cross_tab:debtnotfam_opium04} we exclude debt to family members,
as a robustness test. The impression is still the same, debt seems to
affect the cropping pattern of the farmers.
The impression we get from these cross--tabulations is that the
conditional probability of being an opium producer is greater if the
farmer has debt, relative to not having debt. We investigate whether
this is the case using t--tests for difference of means:
\begin{equation}
\label{t-stat}
t=\frac{\bar{x}-\bar{y}-(\mu_x-\mu_y)}{s_p\sqrt{1/n+1/m}}\sim t_{df}
\end{equation}
where $\bar{x}$ denotes average of opium producing farmers given
debt $>0$, $\bar{y}$ denotes average of opium producing farmers without
debt, $m$ denotes the number of farmers that do not have debt, $n$
denotes the number of farmer that have debt, and finally
\begin{equation*}
s_p=\sqrt{\frac{(n-1)S_x^2+(m-1)S_y^2}{m+n-2}}
\end{equation*}
denotes the pooled sample variance. The t--statistic is t--distributed
with $(m+n-2)$ degrees of freedom. We are interested in testing
whether the mean is different in the two subsamples, hence we apply a
two--sided test:
\begin{equation*}
h_0: \mu_x=\mu_y, h_A: \mu_x\neq \mu_y
\end{equation*}
We use a significance level of 1 \%.
We first test whether there is a difference in the cropping pattern in
2003 for the farmers with outstanding debt from before 2003 relative
to farmers without outstanding debt. The data for the test can be
found in Table \ref{cross_tab:debt_opium03}\footnote{Standard
deviations are not provided in the tables, but are available on
request. }. The test--statistic (\ref{t-stat}) becomes
\begin{equation*}
\label{t_stat:debt_opium03}
\hat{t}=\frac{.84-.75}{\sqrt{.17(1/233+1/671)}}\approx 2.617
\end{equation*}
The critical value is $t^{\ast}_{\alpha/2}=2.576$ with 902 degrees of
freedom, and we can hence reject the null hypothesis that the cropping
pattern is similar for both groups of farmers.
\begin{table}[h]
\caption{Cross--tabulation, debt and opium production 2003}
\label{cross_tab:debt_opium03}
\centering
\begin{tabular}{rrrr}
\hline
& \multicolumn{2}{l}{Loan $<$ 2003} & \\
Opium 03 & 0 & 1 & Total \\
0 & 165 (.25) & 38 (.16) & 203 \\
1 & 506 (.75) & 195 (.84) & 701 \\
Total & 671 (1.0) & 233 (1.0) & 904 \\ \hline
\end{tabular}%
\end{table}
Next we test whether the cropping pattern in 2004 depends on whether
the farmer has taken up a loan in 2003. The reason that we include
this test as well as the former, is twofold. The first reason is that
we have more data on debt taken up in 2003 than debt taken up earlier
than 2003; we have data on who the creditor is. This allows us to do
some more robustness tests, for example we can test whether excluding
debt to family still produces the same result. Second, this allows us
to test the direct effect of debt taken up one year in advance of the
production, while the outstanding debt from before 2003 variable does
not specify which year the debt is from. It is reasonable to assume
that if a farmer has taken up debt in e.g. 1998, and the loan did not
induce opium production at that time, it is unlikely to have any other
effect several years later. Hence, debt taken up one year in advance
gives us a more direct test of our hypothesis.
The test statistic (\ref{t-stat}) becomes
\begin{equation*}
\label{t_stat:debt_opium04}
\hat{t}=\frac{.92-.85}{\sqrt{.10(1/485+1/424))}}\approx 3.55
\end{equation*}
The null hypothesis is rejected, even clearer than in the previous
test. Again this seems to support our general hypothesis, namely that
opium production is partly debt--induced. In addition, it seems to be
that last year's debt is a stronger determinant of opium production,
relative to debt taken up earlier than one year in advance of the
harvesting.
\begin{table}[h]
\caption{Cross--tabulation, debt and opium production 2004}
\label{cross_tab:debt_opium04}
\centering
\begin{tabular}{rrrr}
\hline
& \multicolumn{2}{l}{Loan in 2003} & \\
Opium 04 & 0 & 1 & Total \\
0 & 73 (.15) & 32 (.08) & 105 \\
1 & 412 (.85) & 392 (.92) & 804 \\
Total & 485 (1.0) & 424 (1.0) & 909 \\ \hline
\end{tabular}%
\end{table}
The last t--test is a robustness test. Here debt to family members is
excluded, and we hence look at whether the cropping profile is
different for farmers that have debt to external creditors relative to
debt--free farmers. A priori we expect to find that the effect still
is significant, however we expect to find a lower t--statistic than
the previous test since the variable debt is a superset of debt
without debt to family members.
The test statistic (\ref{t-stat}) is
\begin{equation*}
\label{t_stat:debtnotfam_opium04}
\hat{t}=\frac{.92-.85}{\sqrt{.10(1/513+1/396)}}\approx 3.31
\end{equation*}
Again, the test rejects the null hypothesis.
\begin{table}[h]
\caption{Cross--tabulation, debt (not to family) and opium production 2004}
\label{cross_tab:debtnotfam_opium04}
\centering
\begin{tabular}{rrrr}
\hline
& \multicolumn{2}{l}{Loan in 2003 (not fam.)} & \\
Opium 04 & 0 & 1 & Total \\
0 & 75 (.15) & 30 (.08) & 105 \\
1 & 438 (.85) & 366 (.92) & 804 \\
Total & 513 (1.0) & 396 (1.0) & 909 \\ \hline
\end{tabular}%
\end{table}
This section has shown that the probability of being an opium
producing farmer, conditional on debt, is greater than the probability
of being an opium producing farmer, conditional on not having
debt. The findings are consistent with our main hypothesis, namely
that opium production is partly debt--induced. However, doing simple
correlation analysis as the ones we have just done, may be
misleading. One of the pitfalls is that the dependent variable and the
independent variables are both correlated with a third (latent)
variable, and hence that the correlation we observe is not causal, it
is just a product of (perhaps causal) correlation with a third
(unknown) variable. To remedy this, we perform more thorough tests in
the next section, controlling for other possibly related explanatory
variables.
\newpage
\section{Empirical strategy and results\label{emp_strat}}
Our key equation from the theoretical model states that opium
production in year $t$ is a function of the level of debt taken up at
$t-1$ and the stock of outstanding debt from the years $0,\ldots
,t-2$. In addition the salaam parameter, $\alpha $, is important,
along with price incentives. Price incentives where introduced into
the model by letting the minimum consumption level $\bar{c}$ represent
the consumption obtained from agricultural production without
producing opium, and the model of opium production where then defined
\emph{relative} to the production of other agricultural goods. A
modified version of the key equation is therefore
\begin{equation}
x_{t}=h\left(d_{t-1},\sum_{s=0}^{t-2}d_s,\alpha ,\vec{p}_{t}\right)
\label{key_equation}
\end{equation}
where $d_t$ is the amount of debt taken up at time $t$
($=-(W_t-W_{t-1}))$, using the notation from the theoretical part).
We started considering the moral costs that arise from breaking the
moral/religious norms when producing opium in section
\ref{moral_costs}. As stated, opium and opium production is considered
to be haraam, or forbidden, under Islamic law, and the farmers that
are producing opium are hence deliberately violating this code of
conduct. It is reasonable to assume that violating these moral norms
will induce a ``cost'' for two reasons. First, the farmers are
producing something that they themselves consider to be illegal, and,
depending on the strength of their own religious belief, this induces
a subjective moral burden. Second, opium production may have an impact
on the farmer's reputation in the local community, and it may even
lead to social sanctions. We will hereafter refer to these costs as
moral or religious costs.
Equation (\ref{key_equation}) is a deterministic function governing
the amount of opium production for a given amount of initial debt,
abstracting from considerations like moral and religious
norms. Introducing these moral costs will, since farmers are assumed
to be heterogeneous with respect to the strength of their own religious
belief, give rise to heterogeneity in the amount of produced opium for
given initial debt.
Religious sentiments are not measurable, at least they are not
explicitly considered in the data material we have obtained. We treat
the religious costs as unobservables, i.e. as residuals in the
multinomial logistic regressions. Each individual farmer is assumed
to know their own moral cost term, but from a modelling perspective,
as we do not observe the individual's moral cost term, we consider it
to be drawn individually and independently by the farmers from some
probability distribution.
We add this unobservable part of the utility to the deterministic part
given in (\ref{key_equation}), and get the following equation
\begin{equation*}
x_{i,t}=h\left(d_{t-1},\sum_{s=0}^{t-2}d_s,\alpha
,\vec{p}_{t}\right)+\epsilon _{i,t}
\label{first_econometric_model}
\end{equation*}
As the specification stands now, this seems to be a perfect setting
for an OLS regression. However, several arguments may be put forward
for why this not a good approach. Firstly, in the theoretical part we
showed that the $h$--function may be highly nonlinear, making a linear
(in variables) regression approach inappropriate. Secondly, we do not
have any data on wealth, only debt is registered in our data set, hence
parts of some of the most important explanatory variables are
unobserved (coded as 0). Thirdly, as negative production of opium is
not a possibility, the dependent variable is censored at 0. This makes
the distribution of the error term truncated, and the OLS estimates
will be biased as the error term will have a non--zero expectation for
certain values of the explanatory variables. The third problem we
could remedy using Tobit estimation. Unfortunately, this model does a
poor job in explaining the data, possibly because of nonlinearities in
the $h$--function or the missing parts of the independent variables
(the pseudo-R$^2$ is about .07 in all regressions). In addition, the
Tobit method imposes extremely strong assumptions on the distribution
of the error terms \citep[chapter 16]{cameron2005}. Results from the
Tobit regressions are given in Table \ref{tobit_tabell}.
Another reason why we do not get a good fit may be that moral costs
may introduce fixed costs from switching from production of some other
agricultural crop to opium, as considered in Section
\ref{moral_costs}. This is related to the argument that the dependent
variable is truncated at 0; for many values of the moral cost term the
farmers would like to produce negative amounts of opium. However, as
this is not possible, it is coded as 0. Hence it might be more
interesting to look specifically at the switch from producing opium to
not producing opium, which is what we turn to now.
The approach we choose is to estimate choice probabilities of
producing opium using discrete choice models. The dependent variable
will here be an indicator function for whether the farmer is producing
opium or not. In this way we remedy the problems that arise from the
possibly nonlinear $h $--function. The problem of a censored dependent
variable will also be solved, the distribution of the error term will
no longer be truncated, and we use a more direct approach to address
the problems of fixed cost of starting to produce opium.
\bigskip
We first focus on the choice of opium production in general, where we
look at the binary choice between producing and not producing
opium. After that we look at the different groups of farmers,
modelling the choices using multinomial logistic regressions.
\subsection{Conditional probability of producing opium as a function
of debt\label{binlog}}
We first test our model using a binary logit approach, where the
dependent variable is an indicator function for whether the farmer is
producing opium or not. We are interested in estimating choice
probabilities for the two alternatives, given the characteristics of
the farmers. To accomplish this we run multinomial logistic
regressions, estimating alternative--specific parameters.
A formal specification of the approach is the following: let
\begin{equation*}
y_{t}^{i}= \begin{cases} 1\text{ if $i$ chooses to produce opium in year
$t$} \\ 0\text{ otherwise} \end{cases}
\end{equation*}
and let utility for the different alternatives be given by $U_{ij,t}$,
where $i$ refers to an individual farmer and $j\in\{0,1\}$. As parts
of $U_{ij,t}$ will, by necessity, be unobservable, we can split this
utility into two parts
\begin{equation}
U_{ij,t}=V_{ij,t}+\epsilon_{ij,t}
=\vec{x}^{\prime}_{i,t}\vec{\beta}_j +\epsilon_{ij,t} \label{add_RUM}
\end{equation}
where $V_{ij,t}$ is the representative utility, $\epsilon_{ij,t}$ is a
random error term, $\vec{{x}}_{i,t}$ is characteristics of the farmer
and $\vec{{\beta}}_j$ is the alternative--specific parameters to be
estimated\footnote{All vectors (denoted by bold type) are column
vectors unless otherwise stated. }. The representative utility is
specified to be linear in parameters. For notational simplicity, we
drop the time subscript from now on.
The farmer chooses the alternative that gives him the greatest utility;
he chooses $j$ if and only if $U_{ij}>U_{ik} \, \forall \, k\neq
j$. As we are in a probabilistic framework, $\epsilon_{ij}$ is
unobserved, we will have to model choice probabilities rather that
deterministic choices (the derivation is from \citet{train03}):
\begin{align}
P_{ij}=\Pr[\text{$i$ chooses $j$}]&=\Pr[U_{ij}>U_{ik} \, \forall \, k\neq
j]\notag \\
&=\Pr[V_{ij}+\epsilon_{ij}>V_{ik}+\epsilon_{ik} \, \forall \, k\neq
j]\notag \\
&=\Pr[\epsilon_{ik}-\epsilon_{ij}Q(W_{t-1})]
\end{equation*}
where $V(W_{t-1})$ is the value function defined in the theoretical part
for given inherited debt $W_{t-1}$, $m_i$ is the individual farmer's moral
cost term, and $Q(W_{t.1})$ is the discounted value of a program where
opium is not part of the cropping strategy, given the same inherited
debt $W_{t-1}$. Here I have normalized the moral cost of producing other
crops than opium to zero. In principle this term could be anything, as
long as $m_i$ is scaled appropriately.
The functional form of $P_{ij}$ will obviously depend crucially on the
assumed distribution of the error terms. Following the literature on
discrete choice, we specify the error term $(\epsilon _{ij})$ to be
i.i.d. Extreme Value Type 1 (EV1) distributed. The choice of the
extreme value distribution may at first sight seem somewhat arbitrary,
but there exist good theoretical reasons as to why the error term
should have exactly this distribution. If we believe that
\citet{luce1959}'s independence of irrelevant alternatives (IIA) axiom
holds for the choices in question, \citet{mcfadden1974} proved that
the only random utility maximization model (RUM) that is consistent
with the IIA axiom, is a RUM with extreme value distributed error
terms. Hence we have given an axiomatic justification for the
distribution of the error terms; if we believe that choices are made
according to IIA, the error terms have to be extreme value
distributed\footnote{The IIA property does not have any meaning when
there are only two choices, as here. However, as we later will use
multinomial logit, we introduce the terminology already here. The
reason that the IIA property does not make sense when there are only
two alternatives is that there does not exist any subset of the
choice universe on which the agent can make a choice. Any strict
subset of the choice universe will necessarily contain only one
element, and hence there will not be any choice made by the
agent. The IIA choice axiom states that the choice probabilities
when calculated on any choice set that is a strict subset of the
entire choice universe should not be dependent on the choices not
contained in the subset in question, more formally:
$\Pr_i(S)=\Pr_i(B)\Pr_B(S)$, where $i \in B \subset S$. }. The
distribution of the error term follows directly from behavioral
assumptions, rather than some ad hoc hypothesis on the distribution of
the error term as is often proposed when using an OLS regression
approach. It is also interesting to note that the estimated
coefficients are not very dependent on whether the specification of
the distribution of the error term is EV1 or not, the difference in
estimated coefficients between the binary logit and the binary probit
(where the error term is assumed to be normally distributed), for
example, are almost indistinguishable \citep{dagsvik2006}.
We specify $\vec{x}_n$ to contain the following characteristics (a
priori expectations on the signs are given in parantheses):
\begin{description}
\item[Loan in 2003] $(+)$ Amount of loan taken up in 2003. In the data
set three different currencies are used; Afghani, Pakistani Rupee
(.850) and Iranian Toman (.584). We have converted the loans into
Afghani using the exchange rates given in parentheses. The rates are
the official exchange rates at January 1., 2004 (cash and transfer
average), provided by the Afghan Central Bank. An obvious flaw is
that the exchange rates are likely to vary much at different places
in Afghanistan, depending on distance to banks etc. However, as we
do not have any data on this, we must resort to using official
rates. In addition we would like to have exchange rates from October
2003 (the month when the survey was undertaken), however we have not
been able to obtain these. The variable is scaled down by a factor
of 1000 to obtain more easily interpretable estimates.
\item[Outstanding loan in 2003] $(+)$ The amount of outstanding loan
taken up before 2003, converted to Afghani using the exchange rates
given above. Scaled down by a factor of 1000.
\item[Farmgate price of opium] $(+)$ Farmgate price of opium in the 2003
season. The variable is calculated in the following way:
\begin{enumerate}
\item If the farmer has reported a price, this price is used.
\item If the farmer has not reported a price, the average of the
reported prices in the village is used.
\item If none of farmers in the village have reported a price, the
average in the district is used.
\item If none of the farmers in the district have reported a price,
the average in the area is used.
\item If none of the farmers in the area have reported a price, the
average in the region\footnote{village $<$ district
$<$ area $<$ province $<$ region.} is used.
\end{enumerate}
If no price is calculated after going through this five--step
algorithm, the price variable is set to \texttt{missing}, indicating
that opium is not an option for that particular farmer.
\item[Farmgate price of wheat] $(+/-)$ The farmgate price for wheat in
2003. The variable is calculated using the same algorithm as for the
opium price variable, but one new step is added at the end: if the
variable is still missing after having used the average in the
province, the average of all the prices is used. The reason for this
is that wheat farming is always an option for the farmer, as wheat
can be used for own consumption\footnote{It is reasonable to assume
that opium is not produced for own consumption, at least not
purely for own consumption.}.
\item[Farmgate price of vegetables] $(+/-)$ Farmgate price of
vegetables in 2003. The variable is calculated in the same way as
the wheat variable. Introduced into the utility for the same reason
as the price of wheat, namely to catch opportunity cost of the land.
\item[Price of labor] $(-)$ Calculated using the same method as for
the prices of wheat and vegetables.
\item[Eradication in 2003] Variable indicating whether there has been
eradication of opium crops in the village in the 2003
season. Unfortunately there are many missing observations here, so
we again apply an algorithm to calculate eradication probabilities:
\begin{enumerate}
\item If the village headman have report a response, this response
$\in \{0,1\}$ is used.
\item If the variable is reported as missing, the average in the
district is used.
\item If the variable is still reported as missing, the variable is
coded as 0 (= no eradication).
\end{enumerate}
\item[Own in jeribs] The amount of land owned by the farmer,
introduced to capture to which social classes/wealth groups the
opium producing farmers belong. A problem is that this variable
might be endogenous to the decision we are analyzing, the reason
being that the farmer may own land because they started to produce
opium, while other may be landless because they refused to produce
opium. Whether farmers choose to do this or not, will depend on
their moral cost term, hence some rich farmers will be rich because
they started to produce opium, some will be rich because they are
rich and therefore need not produce opium, while the same is true
for poor farmers: some are poor because they have always been poor,
while some are poor because they have been forced to sell their
land. The problem is hence the lack of time dimension in the
data. As we only have cross--sectional data, we are bound to miss
out on some important and interesting points regarding land
ownership and opium production.
\item[Regional dummies] Dummy variables to catch region--specific
fixed effects\footnote{There are five regions, the division of
provinces into regions follow \citet{unodc_farmers}. The reason
why we do not include lower--level dummies (e.g. province or
district specific dummies) is that introducing such dummies gives
severe estimation problems (collinearity and perfect
predictors).}.
\end{description}
We include prices in 2003 as explanatory variables for production in
2004, i.e. we assume adaptive expectations. This is, as we see it, a
natural assumption about the formation of expectations, since the
planting is done one year in advance. A priori expectations on the
sign of the coefficients are given in parentheses in the list of
variables above. Clearly, we expect a high opium price to have a
positive influence on the probability of producing opium. The farmgate
prices of wheat and vegetables are included to take into account the
opportunity cost of land. We do not have any a priori expectation on
the signs of these two coefficients, the reason being that higher
wheat/vegetable prices have two effects, a ``substitution'' effect and
an ``income'' effect, that can draw in opposite directions. First,
increased wheat price relative to opium will make the probability of
opium production smaller (the substitution effect). Second, increased
wheat price also means that it is harder to earn enough to buy food by
any alternative production, and the farmers are forced to produce the
most profitable crop, opium (the income effect). The eradication
variable is included to control for the risk of eradication. It is
obviously too simple to assume that the risk of eradication is
proportional to the year before, however as the planting is done in
2003, recent eradication in the village may have influenced the
decision on what to crop in 2004. Eradication may also have another
effect; farmers that experienced eradication in 2003 may have problems
repaying their debts due to the loss of their produce, and therefore
roll over the debt to the next harvesting. But due to the salaam
system, the amount of debt will then have increased by a factor of
$\alpha$, and they have to produce more opium to be able to repay the
loan (discussed at length later).
\bigskip
The results are given in Table \ref{binlog_table}. We have run four
logit regressions, the two first include the amount of loan taken up
in 2003 as an explanatory variable, while the two last use loan taken
up in 2003 excluding loans from family members. It is reasonable to
assume that loan from family member have a different effect on opium
production than loans from external creditors, hence we test both
variables. We both include and exclude regional--specific dummies,
regression (2) and (4) include regional--specific dummies.
Surprisingly, the amount of loan taken up in 2003 does not seem to
have an impact on the probability of producing opium, not even when
debt to family members is excluded. The estimated coefficient is
positive as expected in all of the regressions, but the standard error
is too big to make us able to reject the null hypothesis that the
coefficient is equal to zero. The t-value is much closer to being
significant in the case when debt to family members is excluded, but
still not significant at a 5\% level.
Price incentives seem to play an important role, the probability of
producing opium depends negatively on the wage rate in the district
and positively on the observed vegetable price, opium price and wheat
price. As opium is very labor intensive, it is not surprising that a
high wage rate in the area lowers the probability of being an opium
producer. In addition, a high wage rate increases the opportunity cost
of labor, making the use of own household labor to produce opium more
expensive. The price of vegetables has a positive and highly
significant coefficient. The reason for this may be, as stated, that
an increase in the price of food stuff makes the farmers relatively
worse off, and they must produce the most profitable crop to be able
to buy food. The income effect is hence stronger than the substitution
effect. The price of wheat is only significant when regional specific
dummies are included, which may be taken as evidence for that there
are regional--specific shifts in the wheat price, possibly due to that
prices are determined in regional markets. The price of opium is only
significant when regional dummies are excluded, this may be due to the
algorithm we have used to replace missing observations on opium
price. This last step of the algorithm replaces missing observations
with the average of the regional prices, and this may create some
collinearity between opium prices and the regional--specific
dummies. The sign of the opium price coefficient is positive as
expected in all specifications.
The amount of land owned is significant and positive in specification
(1) and (3), and the estimated coefficients are almost equal between
specification (1) and (2), and (3) and (4). Due to that the coefficient
is almost equal across the specifications, and significant in two of
them, we draw the tentative conclusion that opium farmers not
necessarily are parts of the poorest segments of the population, as
the conditional probability of producing opium depends positively on
the amount of land owned.
The most surprising result, however, is that eradication in the area
in 2003 contributes positively to the probability of being an opium
producer in 2004. The effect is also significant at a 5\% level when
regional dummies are included in the logit regressions. As explained
in the theoretical part, this may be because the farmer ends up in a
debt trap if his crops are eradicated, and the farmer is hence forced
to produce opium the next period. It is however important to note that
we have not identified which of farmers that actually experienced the
eradication, eradication here simply means that there has been
eradication in the village or in the area surrounding the village in
2003. Another reason for that eradication increases the probability of
opium production, is that eradication may free farmers to work for
others, creating a boost in production since opium is extremely labor
intensive.
% Table generated by Excel2LaTeX from sheet 'binary logit'
\begin{table}[t]
\caption{Binary logit estimates}
\label{binlog_table}
\begin{tabular}{lrlrlrlrlrrlr}
& \multicolumn{ 2}{c}{(1)} & \multicolumn{2}{c}{(2)} & \multicolumn{ 2}{c}{(3)} & \multicolumn{ 2}{c}{(4)} \\
\hline
\hline
Expl.var. &Coef. &&Coef.&&Coef.&&Coef.\\
\hline
Own in jeribs & .019219 & $^{\ast}$ & .019362 & &.018404 & $^{\ast}$ & .01824 & \\
&(.009) && (.010) && (.009) && (.010) \\
Loan 03 & .002795 && .00129 & \\
&(.002) && (.002) && && \\
Loan 03, not fam. & & & & & .003358 && .002463 & \\
&&&&&(.002) && (.002) \\
Outstanding loan 03 & .008094 && .003064 && .005352& & .00296 & \\
& (.009) && (.005) && (.006) && (.005) \\
Price of vegetables & .209465 & $^{\ast \ast \ast}$ &.232461&$^{\ast \ast \ast}$ & .205245 & $^{\ast \ast}$ &.231087 & $^{\ast \ast \ast}$ \\
&(.074) &&(.070) && (.074) && (.070) \\
Price of wheat & .097982 && .260764 & $^{\ast \ast \ast}$ &.102506 && .26275 & $^{\ast \ast \ast}$ \\
& (.065) && (.087) && (.065) &&(.087) \\
Price of labor & -.003962 & $^{\ast}$ & -.002636 & $^{\ast}$
& -.002998 & $^{\ast \ast \ast}$ & -.002437 &
$^{\ast \ast}$ \\
& (.002) &&(.001) && (.001) && (.001) \\
Price of opium & .000061 & $^{\ast}$ & .000041 &&.000062 & $^{\ast}$ & .00004 & \\
& (.000) && (.000) && (.000) && (.000) \\
Eradication in 03 & .312373 && .665975 & $^{\ast}$&.292798 && .648433 & $^{\ast}$ \\
&(.292) && (.305) && (.292) && (.305) \\
Constant & -.412404 && -1.788991 &&-.55089 && -1.791932 & \\
&(.659) && (1.019) &&(.622) && (1.013) \\
Regional dummies & No && Yes && No && Yes &\\
\hline
Log likelihood & -302.60 && -281.94 && -302.79 && -281.88 &\\
Iterations & 7 && 7 && 6 && 6 &\\
Obs & 909 && 909 && 909 && 909 &\\
\hline
\hline
\end{tabular}
\begin{tabular}{l}
$^{\ast}$ significant at 5\%; $^{\ast \ast}$ significant
at 1\%; $^{\ast \ast \ast}$ significant at .5\%
\end{tabular}
\end{table}
\subsection{Tobit regression}
As stated in the previous section, we have run a Tobit model on the
data. The results are presented in Table \ref{tobit_tabell}. Again we
find that price incentives are important, both the price of opium and
the price labor have a strong impact on the amount of opium
produced. But counter to the previous results neither wheat prices nor
vegetable prices are significant, and the signs have also
changed. Eradication in 2003 also seems to be strongly influencing the
amount of opium produced in 2004, if there has been eradication in the
village the amount of opium produced is shifted up by approximately
1.5 jeribs. The claim that the opium producers are not from the
poorest segments of the population is again verified, the amount of
opium produced depends positively on the amount of land owned, the
effect is significantly different from 0 and the estimated
coefficients almost the same in all the regressions. Neither here nor
in the binary logit case we find that debt influence the cropping
choice, which is counter to widespread belief. But as stated, the
Tobit regressions fits the data poorly, the pseudo-R$^2$ is about .07
in all the regressions (not reported in Table \ref{tobit_tabell}).
% Table generated by Excel2LaTeX from sheet 'tobit'
\begin{table}[t]
\caption{Tobit estimates}
\label{tobit_tabell}
\begin{tabular}{lrlrlrlrl}
& (1) & & (2) & & (3) & & (4) & \\
\hline
\hline
Own in jeribs & .171 & $^{\ast \ast}$ & .170 & $^{\ast \ast}$ & .170 & $^{\ast \ast}$ & .169 & $^{\ast \ast}$ \\
& (.009) & & (.009) & & (.009) & & (.009) & \\
Outstanding loan 03 & .002 & & .002 & & .001 & & .001 & \\
& (.002) & & (.002) & & (.002) & & (.002) & \\
Loan 03 & .001 & & .001 & & & & & \\
& (.000) & & (.000) & & & & & \\
Loan 03, not fam. & & & & & .003 & & .004 & \\
& & & & & (.004) & & (.004) & \\
Price of vegetables & -.131 & & -.085 & & -.134 & & -.089 & \\
& (.090) & & (.091) & & (.09 ) & & (.091) & \\
Price of wheat & -.030 & & -.029 & & -.033 & & -.031 & \\
& (.032) & & (.032) & & (.032) & & (.032) & \\
Price of labor & -.011 & $^{\ast \ast}$ & -.013 & $^{\ast \ast}$ & -.011 & $^{\ast \ast}$ & -.013 & $^{\ast \ast}$ \\
& (.002) & & (.002) & & (.002) & & (.002) & \\
Price of opium & .000 & $^{\ast \ast}$ & .000 & $^{\ast \ast}$ & .000 & $^{\ast \ast}$ & .000 & $^{\ast \ast}$ \\
& (.000) & & (.000) & & (.000) & & (.000) & \\
Eradication in 03 & 1.594 & $^{\ast \ast}$ & 1.406 & $^{\ast \ast}$ & 1.570 & $^{\ast \ast}$ & 1.381 & $^{\ast \ast}$ \\
& (.433) & & (.438) & & (.433) & & (.438) & \\
Constant & 1.041 & & 1.532 & & 1.009 & & 1.473 & \\
& (.866) & & (1.404) & & (.873) & & (1.408) & \\
Regional dummies & No & & Yes & & No & & Yes & \\
\hline
Observations & 909 & & 909 & & 909 & & 909 & \\
\# Left-censored observations & 105 & & 105 & & 105 & & 105 & \\
Log likelihood &-2537.28 &&-2523.48 && -2538.03&& -2524.53& \\
\hline
\hline
\end{tabular}
\begin{tabular}{l}
Standard errors in parentheses\\
$^{\ast}$ significant at 5\%; $^{\ast \ast}$ significant at 1\%
\end{tabular}
\end{table}
\subsection{Discriminating between ``moralists'' and ``opportunists''}
From the results to the binary logit case, we find no significant
effect of debt on the conditional probability of being an opium
producer (see Table \ref{binlog_table}, and the discussion of the
results in Section \ref{binlog}). In this section we modify this
claim, by introducing more ``types'' of opium farmers.
Why does our model fail? We believe that one in general can say that
there are two groups of opium producing farmers. The first group is
the group that we are interested in, the poor farmers who are forced
to produce opium to be able to obtain loans. However, there is also
another group, the ``opportunists'' (introduced in section
\ref{moral_costs}), who produce opium because it is the most valuable
crop. The motivation for these two groups to produce opium is very
different, and to measure the effect that the salaam system and debt
have on the production of opium, we need to be able to distinguish
between the two groups of farmers. One solution to this problem is to
partition the sample of opium producing farmers into groups, where the
selection criterion is the relative amount of opium produced,
following the example in section \ref{moral_costs}. If we find that
different factors are important to farmers in the different groups,
and especially if debt is an important variable for the groups where
the relative amount of opium produced is close to one while
unimportant for the groups that produce little or no opium, this can
be seen as evidence that opium production is debt--induced for the
farmers in the first category. The rationale for this partitioning is
based on three different grounds. First is the extreme convexity in
the costs of producing opium relative to other agricultural goods, we
assume that the profit maximizing level of opium production is
strictly smaller than using the entire amount of arable land available
to a farmer to opium production. To produce one hectare of opium takes
approximately 350 person days, while a hectare of wheat only takes
about 40 person days \citep{strat4}. Since the Afghan farmer often
attributes zero cost household labor, the alternative cost is zero
since female household members often are prohibited from working in
other parts of the economy than household production, there will be a
kink in the cost curve at the point where the farmer needs to hire
non--family labor. Second is an argument about the need for food
security. \citet{mansfield2005} finds that food security deters
households from exclusively cultivating one particular crop, if
possible. Third, as we saw in Section \ref{moral_costs}, when the
farmers have a high moral cost term, passing the threshold level of
debt that induces opium production may lead to huge amounts of
production, as the farmers have refrained from managing their debt the
optimal way due to the moral costs of opium production. But when they
first start to produce opium, the cost from the social stigma becomes
sunk costs, as the moral costs are not related to the amount of opium
produced. This we will utilize in the following to distinguish between
the two groups of farmers. In the example in section
\ref{moral_costs}, we found that moralists either produce nothing or
very much, while the opportunists diversify their production. We
impose the simplifying assumption that the moralists chooses a
relative production level $\in\{0,1\}$, while the opportunists choose
a production level in the interval $(0,1)$. To focus on these groups,
and what the important determinants are for the different groups, we
again apply a multinomial logistic regression approach, modelling
alternative--specific parameters.
The alternative--specific parameters will be defined relative to the
baseline alternative, which here is to not produce opium, since only
relative parameters can be identified. The dependent variable is now a
step function:
\begin{equation*}
y_{i}=
\begin{cases}
0\text{ if $i$ is a farmer but does not produce opium
in 2004}\\
1\text{ if $i$ have a mixed cropping strategy which also
includes opium in 2004}\\
2\text{ if $i$ monocrops opium in 2004}
\end{cases}
\end{equation*}
The derivation of choice probabilities follows directly from section
\ref{binlog}, by letting $j$ take values in $\{0,1,2\}$ instead of
$\{0,1\}$. We use exactly the same set of explanatory variables as in
the binary logit case.
\bigskip
The results from the multinomial logit regressions can be found in
Table \ref{mlogit_table}. We have run two regressions, one including
and one excluding regional--specific dummies. As we are estimating
alternative--specific parameters, and the parameters are given
relative to the 0--alternative, the table contains two columns for
each regression. The first column gives the parameters for the farmers
who produce opium on parts of their land, the ``opportunists'', and
the second column contain the parameters for the group who devote all
their land to opium production, the group for which we claim that
opium production is debt--induced.
We first note that eradication in 2003 has a different effect on the
two groups, which may explain the findings from the binary logit
case. Eradication has a much stronger effect on the group that devote
all their land to opium than the other, which can be seen as evidence
for the story that farmers who experience eradication will have to
increase their production even more the next year to be able to repay
their debts. Also debt, excluding debt to family members, has a strong
and positive effect for the farmers in category 2, supporting that
opium production is debt--induced for these farmers: the conditional
probability of ending up as a farmer who monocrops opium is strictly
increasing in the amount of debt taken up in 2003, controlled for the
amount of the land the household owns. We also see that the amount of
land affects negatively the probability of ending up as a category 2
farmer. This may be due to two reasons, one is that since production
costs are highly convex for opium relative to other crops, more land
will reduce the probability of the farmer devoting all his land to
opium. The other reason that we get this result is that poor farmers
who produce opium more often do it out of necessity, they devote all
their arable land to production, while richer farmers produce at a
level where they maximize profits.
Price incentives are important for both groups. The price of labor
seems to influence only the choice of ending up in category 1 relative
to not producing opium, i.e. if the price of labor goes up these
farmers switch to producing other crops, while the effect on the
category 2 farmers is much smaller. Again we can interpret this as
evidence for the story that their production is debt--induced, as the
supply of opium for this group is relatively inelastic to changes in
wages.
% Table generated by Excel2LaTeX from sheet 'multinomial logit'
\begin{table}[t]
\caption{Multinomial logit estimates}
\label{mlogit_table}
\begin{tabular}{lrlrlrlrl}
&\multicolumn{ 4}{c}{(1)} &\multicolumn{ 4}{c}{(2)} \\
\hline
\hline
&Polycrop &&Monocrop&&Polycrop &&Monocrop&\\
\hline
Own in jeribs &.025015 & $^{\ast}$ &-.105485 & $^{\ast \ast \ast}$ & .025252 & $^{\ast}$ & -.107302 & $^{\ast \ast \ast}$ \\
&(.010) &&(.023) &&(.011) &&(.024) &\\
Outstanding loan 03 &.00449 && .007364 && .002309 && .005015 &\\
&(.006) &&(.006) &&(.005) &&(.005) &\\
Loan 03, not fam. & .002679 && .009009 & $^{\ast \ast}$ & .002001 && .007404 & $^{\ast}$ \\
&(.002) &&(.003) &&(.002) &&(.003) &\\
Price of vegetables & .201512 & $^{\ast \ast}$ & .209862 & $^{\ast}$ & .226104 & $^{\ast \ast \ast}$ & .243306 & $^{\ast \ast \ast}$ \\
&(.074) &&(.083) &&(.070) &&(.081) &\\
Price of wheat & .074009 && .19622 & $^{\ast \ast}$ & .239755 & $^{\ast \ast}$ & .362036 & $^{\ast \ast \ast}$ \\
& (.068) && (.073) && (.087) && (.092) &\\
Price of labor & -.002881 & $^{\ast \ast \ast}$ & -.002347 && -.002411 & $^{\ast \ast \ast}$ & -.001449 &\\
& (.001) && (.002) && (.001) && (.002) &\\
Price of opium & .000057 & $^{\ast}$ & .000095 & $^{\ast \ast \ast}$ & .000051 && -.000007 &\\
& (.000) && (.000) && (.000) && (.000) &\\
Eradication in 03 & .157325 && .757856 & $^{\ast}$ & .509381 && 1.0502 & $^{\ast \ast \ast}$ \\
& (.297) && (.342) && (.309) && (.361) &\\
Constant & -.51147 && -3.08238 & $^{\ast \ast \ast}$ & -2.081076 & $^{\ast}$ & -2.699812 & $^{\ast}$ \\
& (.630) && (.805) && (1.027) && (1.229) &\\
Regional dummies & No &&&& Yes &&&\\
\hline
Log likelihood & -634.49 &&&& -603.01 &&&\\
Iterations & 6 &&&& 6 &&&\\
Obs & 909 &&&& 909 &&&\\
\hline
\hline
\end{tabular}
\begin{tabular}{l}
Standard errors in parentheses \\
$^{\ast}$ significant at 5\%; $^{\ast \ast}$ significant
at 1\%; $^{\ast \ast \ast}$ significant at .5\%
\end{tabular}
\end{table}
\subsubsection{Test of the implied correlation structure for the error
terms}
There is however one potential problem with the multinomial logit
approach, namely the assumed independence of the error terms across
alternatives. It might be reasonable to assume that the error terms
for alternative 1 and 2 share some features and hence are correlated,
as they both involve production of opium. This correlation structure
may be captured in a nested logit model, and we estimate this version
of the model to test whether the multinomial logit approach is
appropriate, or whether we need to employ more sophisticated
methods. In the nested logit approach, we can think of the choices as
being made sequentially: first the farmer decides whether or not to
produce opium, and then he decides on the amount. This way of thinking
about the choices is somewhat counter to how I presented them earlier,
but the important thing here is not the tree structure of the problem
implied by the nested logit, it is to analyze the correlation
structure among the random error terms.
The nested logit probabilities are found in the following way. Let the
distribution of the error terms be given by the generalized extreme
value distribution (the derivation is from \citet{dagsvik2006})
\begin{equation*}
\Pr\left[\epsilon_{0}\leq x_0,\ldots,\epsilon_{J}\leq x_J \right]=F(\vec{x})= \exp\left(-G(\exp(-x_0),\exp(-x_1),\ldots,\exp(-x_J)) \right)
\end{equation*}
where $G(\cdot)$ follows the standard assumption in
\citet{mcfadden1978}. $F(\vec{x})$ is a joint distribution function
whose one--dimensional marginal distributions are extreme value
distributions \citep{mcfadden2001}. If the utility function is an
additative RUM (as in equation (\ref{add_RUM}) here),
\citet{mcfadden1978} proved that
\begin{equation*}
\Pr(U_{ij}=\max_k(U_{ik}))=\frac{\exp(V_{ij})G_j(\exp(V_{i1}),\ldots,\exp(V_{iJ}))}
{G(\exp(V_{i1}),\ldots,\exp(V_{iJ}))}
\end{equation*}
If we let
\begin{equation*}
G(x)=x_0+\left(x_1^{1/\tau}+x_2^{1/\tau}\right)^{\tau}
\end{equation*}
we have the nested model with correlation between alternative 1 and 2,
$\rho(\epsilon_1,\epsilon_2)=1-\tau^2$, and no correlation across
nests, $\rho(\epsilon_0,\epsilon_j)=0$ for $j=1,2$. Following McFadden
(1978) and \citet{dagsvik2006} we find that the choice probabilities
are given by
\begin{equation*}
P_{i0}=\frac{\exp(V_{i0})} {\exp(V_{i0})+\left[\exp(V_{i1})^{1/\tau}+\exp(V_{i2})^{1/\tau}\right]^{\tau}}
\end{equation*}
and
\begin{equation*}
P_{ij}=\frac{\left[\exp(V_{i1})^{1/\tau}+\exp(V_{i2})^{1/\tau}\right]^{\tau-1}\exp(V_{ij}/\tau)}{\exp(V_{i0})+(\exp(V_{i1})^{1/\tau}+\exp(V_{i2})^{1/\tau})^{\tau}}
\end{equation*}
for $j=1,2$. We immediately see that if $\tau=1$ the standard
multinomial case emerges. Hence the multinomial logit model is a
special case of the nested model, and testing whether $\tau \neq 1$
will show whether using the non--nested multinomial model is
appropriate or not.
Importantly, the Stata \texttt{nlogit} command, which I have used in
the estimation, estimates \citet{daly1987}'s non--normalized nested
logit model (NNNL), which departs from the \citet{mcfadden1974}'s
random utility maximization nested logit model (RUMNL) in that the
inclusive value terms are not normalized by the dissimilarity
parameter(s) \citep{heiss2002}. Here $\tau$ is the dissimilarity
parameter. \citet{koppelman1998} shows that only in very special cases
the NNNL model is consistent with random utility maximization, and
they also shows that estimates of the coefficients may be very
different under the two different models. \citet{heiss2002}, however,
shows that if only alternative--specific coefficients are estimated
(as here), then the model is consistent with utility maximization. He
also shows that in this case the log likelihood and the dissimilarity
parameter(s) will be the same as if the model was estimated using the
\citet{mcfadden1974} approach, but the coefficients will be scaled
differently (they will be proportional to the coefficients from the
RUMNL model by a factor equal to the inverse of the dissimilarity
parameter). As we only include the nested multinomial logit model as a
test on whether the normal non--nested approach used earlier is
sufficient, and this test only uses the calculated dissimilarity
parameter and the estimated log likelihood, which are similar in the
two models given that only alternative--specific parameters are
estimated, I do not go deeper into this.
The test of the assumed independence of the error terms across
alternatives, is a likelihood ratio test of whether the dissimilarity
parameter is significantly different from 1. The test statistics is
\begin{equation}
\text{LR}=-2\left[\ln \left(L\left(\vec{\beta}^{\text{R}}\right)\right)-\ln(L(\vec{\beta}))\right]\sim
\chi^2_{\text{number of restrictions}} \label{likelihood_test}
\end{equation}
where $\ln(L(\vec{\beta}^{\text{R}})$ is the log likelihood for the
model with restrictions and $\ln(L(\vec{\beta}))$ is the
log likelihood for the unrestricted model. Here we impose one
restriction, and if we choose significance level $\alpha=.05$, the
critical value is 3.84. As we will see in the next section, we can not
reject the null hypothesis that the dissimilarity parameter is equal
to one in any of the specifications, hence the multinomial approach is
sufficient.
\bigskip
The results from the nested logit models can be found in Table
\ref{nested_logit_table}. The purpose of including this specification
is to test whether the multinomial approach is valid, or whether the
imposed IIA assumption violates the correlation structure in the
random error terms.
To be able to estimate the model in Stata, I have had to convert my
previous multinomial logistic regression to a conditional logit form,
using alternative--specific dummies. For this reason I also include
the previous multinomial logistic regression results in Table
\ref{nested_logit_table} (regressions (1) and (2)), as a test that the
inclusion of the dummy variables does not alter any of the results
(and as a test that my computer code does not include any
mistakes). Column (3) and (4) of the table gives the nested logit
estimates.
The likelihood ratio test gives the following results: for the model
without regional dummies, the test statistic from
(\ref{likelihood_test}) becomes
\begin{equation*}
\hat{\text{LR}}=-2[-634.49--633.73]=1.52<3.84
\end{equation*}
For the model with regional dummies,
\begin{equation*}
\hat{\text{LR}}=-2[-603.01--602.99]=0.04<3.84
\end{equation*}
Hence the test cannot reject the null hypotheses that $\tau=1$. For
this reason we safely continue to use the non--nested multinomial
model rather than the nested.
% Table generated by Excel2LaTeX from sheet 'nested logit'
\begin{landscape}
\begin{table}
\caption{Nested logit estimates}
\label{nested_logit_table}
\begin{tabular}{llrlrrlrrlrrlr}
&&\multicolumn{ 3}{c}{(1)} &\multicolumn{ 3}{c}{(2)} &\multicolumn{ 3}{c}{(3)} &\multicolumn{ 3}{c}{(4)} \\
\hline
\hline
Variables &&Coef. && \multicolumn{1}{c}{SE} &Coef.&& \multicolumn{1}{c}{SE} &Coef.&& \multicolumn{1}{c}{SE} &Coef. && \multicolumn{1}{c}{SE} \\
\hline
const $\times$ &Polycrop&-.51147 &&(.630)&-2.081076 & $^{\ast}$ &(1.027) &-.179891 &&(.271)&-1.744335 &&(1.703)\\
&Monocrop &-3.08238 & $^{\ast \ast \ast}$ &(.805) &-2.699812 & $^{\ast}$ &(1.229) &-2.826832 &&(.548) &-2.357403 &&(1.855) \\
Own in jeribs $\times$ & Polycrop &.025015 & $^{\ast \ast}$ &(.010) &.025252 & $^{\ast}$ &(.011) &.014185 & $^{\ast \ast}$ &(.006) &.021869 &&(.017) \\
&Monocrop &-.105485 & $^{\ast \ast \ast}$ & (.023) & -.107302 & $^{\ast \ast \ast}$ & (.024) & -.114715 && (.020) & -.110506 & $^{\ast \ast \ast}$ & (.027) \\
Outstanding loan $\times$ & Polycrop &.00449 &&(.006) &.002309 &&(.005) &.001447 &&(.003) &.001794 &&(.005) \\
&Monocrop &.007364 &&(.006) &.005015 &&(.005) &.004253 &&(.003) &.004474 &&(.005) \\
Loan 03, not family $\times$ & Polycrop &.002679 &&(.002) &.002001 &&(.002) &.000748 &&(.001) &.001551 &&(.003) \\
&Monocrop &.009009 & $^{\ast \ast}$ &(.003) &.007404 & $^{\ast}$ &(.003) &.006742 & $^{\ast \ast}$ &(.002) &.006928 & $^{\ast}$ &(.003) \\
Price of vegetables $\times$ & Polycrop & .201512 & $^{\ast \ast}$ & (.074) & .226104 & $^{\ast \ast \ast}$ & (.070) & .076261 && (.050) & .182833 && (.199) \\
&Monocrop &.209862 & $^{\ast}$ &(.083) &.243306 & $^{\ast \ast \ast}$ &(.081) &.077909 &&(.066) &.198481 &&(.211) \\
Price of wheat $\times$ &Polycrop & .074009 && (.068) & .239755 & $^{\ast \ast}$ & (.087) & .013468 && (.033) & .190417 && (.228) \\
&Monocrop &.19622 & $^{\ast \ast}$ &(.073) &.362036 & $^{\ast \ast \ast}$ &(.092) &.138189 & $^{\ast \ast \ast}$ &(.043) &.31301 &&(.228) \\
Price of labor $\times$ & Polycrop &-.002881 & $^{\ast \ast \ast}$ &(.001) & -.002411 & $^{\ast \ast \ast}$ &(.001) &-.00111 &&(.001) &-.001964 &&(.002) \\
&Monocrop &-.002347 &&(.002) &-.001449 &&(.002) &-.000365 &&(.002) &-.000934 &&(.003) \\
Price of opium $\times$ &Polycrop &.000057 & $^{\ast}$ &(.000) &.000051 && (.000) &.000018 &&(.000) &.000043 &&(.000) \\
&Monocrop &.000095 & $^{\ast \ast \ast}$ &(.000) &-.000007 &&(.000) &.000061 & $^{\ast}$ &(.000) & -.000016 &&(.000) \\
Eradication in 2003 $\times$ & Polycrop & .157325 && (.297) & .509381 && (.309) & -.013799 && (.132) & .388 && (.590) \\
& Monocrop & .757856 & $^{\ast}$ & (.342) & 1.0502 & $^{\ast \ast \ast}$ & (.361) & .582847 & $^{\ast \ast}$ & (.217) & .929943 && (.613) \\
Regional dummies &&No &&&Yes &&&No &&&Yes &&\\
$\tau$ &&--- &&&--- &&&2.604634 &&(1.387) &1.232673 &&(1.263) \\
\hline
Log likelihood && -634.49 &&&-603.01 &&&-633.73 &&&-602.99 &&\\
Iterations &&6 &&&7 &&&306 &&&12 &&\\
Obs &&909 &&&909 &&&909 &&&909 &&\\
\hline
\hline
\end{tabular}
\begin{tabular}{l}
$^{\ast}$ significant at 5\%; $^{\ast \ast}$ significant
at 1\%; $^{\ast \ast \ast}$ significant at .5\%
\end{tabular}
\end{table}
\end{landscape}
\newpage
\section{Conclusions\label{conclusions} }
This master thesis has analyzed whether or not opium production in
Afghanistan is debt--induced, i.e. whether the cropping strategy of
indebted farmers are different from other farmers. The main reason for
studying this is that, to my knowledge, a thorough statistical
analysis of this question has not yet been done. Many studies of a
more qualitative nature have examined the question, and there seems to
be a broad consensus in the literature that credit and opium
production is interlinked
\citep{bulletin1999,mansfield_myth,mansfield_diversity2004,brr2004,strat3,unodc_opec03}. However,
this story is far from as obvious as it may seem to be by looking at
correlation tables between debt and opium production, where the
conditional probability of being an opium producer is found to
significantly higher if the respondend has debt (see section
\ref{description_data}). When controlling for price incentives, social
class and eradication risk, we find no significant effect of debt on
the conditional probability of being an opium producer (table
\ref{binlog_table}). It is interesting to note that price incentives,
especially prices on other agricultural crops, and eradication are
important determinants of opium production. Eradication in the village
in 2003 significantly \emph{increases} the probability of opium
production in 2004. Several possible explanations to this have been
given in Section \ref{binlog}, among them is that eradication may free
labor, which is important since opium production is extremely
labor--intensive. We also find that the more land the farmer owns,
i.e. the wealthier he is, the higher is the probability that he is an
opium producer. We hence find a somewhat different picture than what
is usually presented, here the opium farmer responds to price
incentives, he is not in the poorest segments of the population, and
debt seems to be unimportant for the choice of cropping strategy.
The reason why we do not find that the conditional probability depends
on debt, is that farmers have two different (but often overlapping)
incentives to produce opium. First, as it is the most valuable crop,
farmers produce it to maximize the household's utility. But opium
production is both illegal and anti--Islamic, hence there exist both
social and moral costs to producing opium, which constrain the number
of farmers choosing to produce opium for profit. Second, farmers
produce opium to obtain loans, as opium production often is a
prerequisite to be granted salaam loans, loans that are to be repaid
in kind.
When we introduce moral costs into our theoretical model, we find that
the heterogeneity in moral costs creates two subpopulations of opium
farmers, the ``opportunists'' that maximize profit and the
``moralists'' that produces opium out of necessity. We also find that
the two groups will have a different cropping strategy, which makes us
able to distinguish them empirically: the ``moralists'' will produce
zero opium until their accumulated debt reaches a tipping point, and
when this point is reached they will produce at maximum capacity. The
``opportunists'' however, will find it optimal to diversify their
production, producing opium as well as other crops.
To separate the two effects we therefore estimate choice probabilities
for ending up as a monocropping opium farmer, relative to producing
some opium or not producing opium. This model gives very intuitive
results: for the monocropping opium farmers debt is an important
determinant, while for the others debt is unimportant. We also find
that the cost of labor is important for the ``opportunists'', while
not important for the ``moralists''. Finally we find that eradication
in the village is an important determinant of opium production only
for the ``moralists'', supporting that these farmers have experienced
a bad shock that have increased their debt beyond the tipping point.
\newpage
\addcontentsline{toc}{section}{References}
\bibliography{fredrikhw}
\newpage
\appendix
\section{Computer code}
I have used Stata for estimation. The code used to create Tables
\ref{binlog_table}--\ref{nested_logit_table} is given below. The trick
of using constraints to avoid specifing the upper level utility in the
nested logit model is from \citet{heiss2002}.
\subsection{Binary logit}% simple_logit.do
\begin{tiny}
\begin{verbatim}
use "FIS_full.dta";
egen opiumprice1=mean(opiumprice), by(id_region);
replace opiumprice=opiumprice1 if opiumprice==.;
egen eradication1=mean(eradicationin2003), by(id_district);
replace eradicationin2003=eradication1 if eradicationin2003==.;
replace eradicationin2003=0 if eradicationin2003==.;
drop eradication1;
gen loan_notfam=loan_amount_2003-_29_amount_Family;
egen arbeidsdag1=mean(arbeidsdag);
replace arbeidsdag=arbeidsdag1 if arbeidsdag==.;
replace loan_notfam=loan_notfam/1000;
replace outstandingloan_amount=outstandingloan_amount/1000;
replace loan_amount_2003=loan_amount_2003/1000;
log using "simple_logit", replace text;
logit opium2004_dummy owninjeribs loan_amount_2003 outstandingloan_amount vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
if farmer_production_2004>0 & farmer_production_2004!=.;
logit opium2004_dummy owninjeribs loan_amount_2003 outstandingloan_amount vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
regionc1-regionc4 if farmer_production_2004>0 & farmer_production_2004!=.;
logit opium2004_dummy owninjeribs loan_notfam outstandingloan_amount vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
if farmer_production_2004>0 & farmer_production_2004!=.;
logit opium2004_dummy owninjeribs loan_notfam outstandingloan_amount vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
regionc1-regionc4 if farmer_production_2004>0 & farmer_production_2004!=.;
log c;
\end{verbatim}
\end{tiny}
\subsection{Tobit regression}% tobit_regr.do
\begin{tiny}
\begin{verbatim}
use "FIS_full.dta";
egen opiumprice1=mean(opiumprice), by(id_region);
replace opiumprice=opiumprice1 if opiumprice==.;
egen eradication1=mean(eradicationin2003), by(id_district);
replace eradicationin2003=eradication1 if eradicationin2003==.;
replace eradicationin2003=0 if eradicationin2003==.;
drop eradication1;
gen loan_notfam=loan_amount_2003-_29_amount_Family;
egen arbeidsdag1=mean(arbeidsdag);
replace arbeidsdag=arbeidsdag1 if arbeidsdag==.;
gen rel04=poppy_production_2004/farmer_production_2004;
gen poppycat=.;
replace poppycat=0 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004==0;
replace poppycat=1 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004>0 & rel04<1;
replace poppycat=2 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004>0 & rel04==1;
replace loan_amount_2003=loan_amount_2003/1000;
replace loan_notfam=loan_notfam/1000;
replace outstandingloan_amount=outstandingloan_amount/1000;
log using "tobit", replace text;
tobit poppy_production_2004 owninjeribs outstandingloan_amount loan_amount_2003 vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
if farmer_production_2004>0 & farmer_production_2004!=., ll;
outreg using tobit, se replace;
tobit poppy_production_2004 owninjeribs outstandingloan_amount loan_amount_2003 vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
regionc1-regionc4 if farmer_production_2004>0 & farmer_production_2004!=., ll;
outreg using tobit, se append;
tobit poppy_production_2004 owninjeribs outstandingloan_amount loan_notfam vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
if farmer_production_2004>0 & farmer_production_2004!=., ll;
outreg using tobit, se append;
tobit poppy_production_2004 owninjeribs outstandingloan_amount loan_notfam vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
regionc1-regionc4 if farmer_production_2004>0 & farmer_production_2004!=., ll;
outreg using tobit, se append;
log c;
\end{verbatim}
\end{tiny}
\subsection{Multinomial logit}% multinomial_logit.do
\begin{tiny}
\begin{verbatim}
use "FIS_full.dta";
egen opiumprice1=mean(opiumprice), by(id_region);
replace opiumprice=opiumprice1 if opiumprice==.;
egen eradication1=mean(eradicationin2003), by(id_district);
replace eradicationin2003=eradication1 if eradicationin2003==.;
replace eradicationin2003=0 if eradicationin2003==.;
drop eradication1;
gen loan_notfam=loan_amount_2003-_29_amount_Family;
egen arbeidsdag1=mean(arbeidsdag);
replace arbeidsdag=arbeidsdag1 if arbeidsdag==.;
gen rel04=poppy_production_2004/farmer_production_2004;
gen poppycat=.;
replace poppycat=0 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004==0;
replace poppycat=1 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004>0 & rel04<1;
replace poppycat=2 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004>0 & rel04==1;
replace loan_amount_2003=loan_amount_2003/1000;
replace loan_notfam=loan_notfam/1000;
replace outstandingloan_amount=outstandingloan_amount/1000;
log using "multinomial_logit", replace text;
mlogit poppycat owninjeribs outstandingloan_amount loan_notfam vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
regionc1-regionc4, basecategory(0);
mlogit poppycat owninjeribs outstandingloan_amount loan_notfam vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003, basecategory(0);
mlogit poppycat owninjeribs outstandingloan_amount loan_amount_2003 vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003
regionc1-regionc4, basecategory(0);
mlogit poppycat owninjeribs outstandingloan_amount loan_amount_2003 vegetableprice wheatprice arbeidsdag opiumprice eradicationin2003, basecategory(0);
log c;
\end{verbatim}
\end{tiny}
\subsubsection{Nested multinomial logit}% nested_logit.do
\begin{tiny}
\begin{verbatim}
use "FIS_full.dta";
egen opiumprice1=mean(opiumprice), by(id_region);
replace opiumprice=opiumprice1 if opiumprice==.;
egen eradication1=mean(eradicationin2003), by(id_district);
replace eradicationin2003=eradication1 if eradicationin2003==.;
replace eradicationin2003=0 if eradicationin2003==.;
gen loan_notfam=loan_amount_2003-_29_amount_Family;
egen arbeidsdag1=mean(arbeidsdag);
replace arbeidsdag=arbeidsdag1 if arbeidsdag==.;
drop opiumprice1 eradication1 arbeidsdag1 provc1-provc29 id_district
id_province id_region id_village opiumprice_mean_village opiumprice_mean_district
opiumprice_difference_village opiumprice_difference_district outstandingloanyear;
gen rel04=poppy_production_2004/farmer_production_2004;
gen poppycat=.;
replace poppycat=0 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004==0;
replace poppycat=1 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004>0 & rel04<1;
replace poppycat=2 if farmer_production_2004>0 & farmer_production_2004!=. & poppy_production_2004>0 & rel04==1;
replace loan_notfam=loan_notfam/1000;
replace outstandingloan_amount=outstandingloan_amount/1000;
expand 3;
sort id;
gen seq=mod(_n-1,3);
gen valg=0;
replace valg=1 if poppycat==0 & seq==0;
replace valg=1 if poppycat==1 & seq==1;
replace valg=1 if poppycat==2 & seq==2;
gen asc_1=0;
gen asc_2=0;
replace asc_1=1 if seq==1;
replace asc_2=1 if seq==2;
gen owninjeribs_1=owninjeribs*asc_1;
gen owninjeribs_2=owninjeribs*asc_2;
gen outstandingloan_amount_1=outstandingloan_amount*asc_1;
gen outstandingloan_amount_2=outstandingloan_amount*asc_2;
gen loan_notfam_1=loan_notfam*asc_1;
gen loan_notfam_2=loan_notfam*asc_2;
gen vegetableprice_1=vegetableprice*asc_1;
gen vegetableprice_2=vegetableprice*asc_2;
gen wheatprice_1=wheatprice*asc_1;
gen wheatprice_2=wheatprice*asc_2;
gen arbeidsdag_1=arbeidsdag*asc_1;
gen arbeidsdag_2=arbeidsdag*asc_2;
gen opiumprice_1=opiumprice*asc_1;
gen opiumprice_2=opiumprice*asc_2;
gen eradicationin2003_1=eradicationin2003*asc_1;
gen eradicationin2003_2=eradicationin2003*asc_2;
gen regionc1_1=regionc1*asc_1;
gen regionc1_2=regionc1*asc_2;
gen regionc2_1=regionc2*asc_1;
gen regionc2_2=regionc2*asc_2;
gen regionc3_1=regionc3*asc_1;
gen regionc3_2=regionc3*asc_2;
gen regionc4_1=regionc4*asc_1;
gen regionc4_2=regionc4*asc_2;
egen nothing=fill(1 0 0 1 0 0);
cons define 1 nothing = 0;
nlogitgen o_vs_not_o = seq(notop:0,op:1|2);
log using "nested_logit", replace text;
clogit valg asc_* owninjeribs_* outstandingloan_amount_* loan_notfam_* vegetableprice_* wheatprice_* arbeidsdag_* opiumprice_* eradicationin2003_*
regionc1_* regionc2_* regionc3_* regionc4_*, group(id);
nlogit valg (seq= asc_* owninjeribs_* outstandingloan_amount_* loan_notfam_* vegetableprice_* wheatprice_* arbeidsdag_* opiumprice_* eradicationin2003_*
regionc1_* regionc2_* regionc3_* regionc4_*)(o_vs_not_o=nothing), group(id) const(1) ivc(notop=1 op=1);
clogit valg asc_* owninjeribs_* outstandingloan_amount_* loan_notfam_* vegetableprice_* wheatprice_* arbeidsdag_* opiumprice_* eradicationin2003_*, group(id);
nlogit valg (seq= asc_* owninjeribs_* outstandingloan_amount_* loan_notfam_* vegetableprice_* wheatprice_* arbeidsdag_* opiumprice_* eradicationin2003_*)
(o_vs_not_o=nothing), group(id) const(1) ivc(notop=1 op=1);
nlogit valg (seq= asc_* owninjeribs_* outstandingloan_amount_* loan_notfam_* vegetableprice_* wheatprice_* arbeidsdag_* opiumprice_* eradicationin2003_*
regionc1_* regionc2_* regionc3_* regionc4_*)(o_vs_not_o=nothing), group(id) const(1) ivc(notop=1);
nlogit valg (seq= asc_* owninjeribs_* outstandingloan_amount_* loan_notfam_* vegetableprice_* wheatprice_* arbeidsdag_* opiumprice_* eradicationin2003_*)
(o_vs_not_o=nothing), group(id) const(1) ivc(notop=1);
log c;
\end{verbatim}
\end{tiny}
\end{document}