Tariff Evasion and Customs Corruption:
Does Pre-Shipment Inspection Help?
José Anson
Olivier Cadot
Marcelo Olarreaga§
Abstract
This paper provides a new approach to the evaluation of pre-shipment
inspection (PSI) programs as ways of improving tariff-revenue collec-
tion and reducing fraud when customs administrations are corrupt.
We build a model highlighting the contribution of surveillance firms to
the generation of information and describing how incentives for fraud
and collusive behaviour between importers and customs are affected
by the introduction of PSI. It is shown theoretically that the intro-
duction of PSI has an ambiguous effect on the level of customs fraud.
Empirically, our econometric results suggest that PSI reduced fraud
in the Philippines; it increased it in Argentina and had not significant
impact in Indonesia.
JEL classification numbers: F10, F11, F13
Keywords: Trade, Tariff Revenue, Corruption, Pre Shipment Inspec-
tion.
This research was produced as part of a World Bank research program on Customs
corruption and Pre-Shipment Inpsection services. We are grateful to Nigel Balchin, Caro-
line Freund, Fred Herren, Francis Ng, Alessandro Nicita, Jerzy Rozanski, Maurice Schiff,
Shang-Shin Wei, Luc De Wulf and participants at seminars at the Troisieme Cycle Ro-
mand in Crans-Montana and the World Bank for very helpful comments and suggestions.
We retain however sole responsibility for any remaining error. The views expressed here
are those of the authors and should not be attributed to the institutions to which they are
affiliated.
HEC Lausanne; e-mail: jose.anson@hec.unil.ch.
HEC Lausanne, CERDI and CEPR; olivier.cadot@hec.unil.ch.
§World Bank and CEPR; molarreaga@worldbank.org
N -T S
First introduced in Zaire in 1963 and adopted since then by over fifty
countries worldwide, Pre-Shipment Inspection (PSI) consists of requiring
imports to be inspected by a private surveillance company at embarkation
ports or airports or in the exporter firms' premises, instead of just at the im-
porting country's customs. Originally, PSI was intended to fight the use of
overinvoiced imports to evade capital controls. As capital controls were pro-
gressively phased out, the attention of governments shifted to import-tariff
evasion and, starting with Indonesia's program in 1985, the mission assigned
to PSI accordingly changed to curbing underinvoicing.
The objective of this paper is to provide a new approach to the evaluation
of PSI programs as ways of reducing customs fraud. After providing some
inconclusive prima facie evidence for sixteen developing countries for which
we had trade data before and after the introduction of PSI services, we adopt
a more structural approach. We first set up a simple game-theoretic model
of tariff evasion and customs effort generating testable predictions about
the relationship between tariff rates and evasion. The model relies on an
information-production framework developed by Aghion and Tirole (1997)
and applied to corruption problems by Anson (2003). The idea is essentially
that customs must spend costly resources assessing the value of shipments
and that the outcome of their effort is stochastic (that is, higher levels of
effort only reduce the likelihood of errors). This idea seems particularly well
suited to a customs-operation context where officers must determine how
thoroughly they inspect shipments knowing that exact valuation may be
elusive even after careful inspection (especially for capital equipment which
requires technical knowledge to be properly valued). In this context, what
PSI does is to provide additional information on shipment value. In a per-
fect world, this information would only be used by the client government to
control fraud. But this additional information is now available to a poten-
tially corrupt customs officers which can use it to extract higher rents from
importers through bribery arrangements, leading to higher customs fraud.
Thus, whether PSI increases or reduces customs fraud becomes an em-
pirical question. We tested our structural model on panels of disaggregated
trade data for three developing countries that have used PSI services (Ar-
gentina, Philippines and Indonesia). Our estimates suggest that customs
fraud increased in Argentina after the introduction of PSI services, it was
reduced in the Philippines and there was no impact in the case of Indonesia.
1 Introduction
First introduced in Zaire in 1963 and adopted since then by over fifty coun-
tries worldwide, Pre-Shipment Inspection (PSI) consists of requiring imports
to be inspected by a private surveillance company1 at embarkation ports
or airports or in the exporter firms' premises, instead of just at the im-
porting country's customs. Originally, PSI was intended to fight the use of
overinvoiced imports to evade capital controls. As capital controls were pro-
gressively phased out, the attention of governments shifted to import-tariff
evasion and, starting with Indonesia's program in 1985, the mission assigned
to PSI accordingly changed to curbing underinvoicing.
Whether they look for over- or underinvoiced imports, surveillance com-
panies are entrusted by client governments with the assessment of an im-
portant tax base and become, de facto, quasi tax collectors, even if tariff
collection remains de jure under state authority. Although private tax col-
lection is, by itself, an old practice,2 outsourcing such a key state function to
the private sector can nonetheless be perceived by governments as a major
delegation of authority, compounded by a sense of loss of sovereignty if those
companies are foreign ones. To be politically acceptable, thus, PSI needs to
be justified by strong arguments (for a brief review of those arguments, see
Ramirez, 1992 or Byrne, 1995; on the difficulties encountered by the WTO
Agreement on Customs Valuation in developing countries, see Goorman and
1The market is dominated by a small number of companies: Geneva-based Société
Générale de Surveillance (SGS) and Cotecna, Paris-based Bureau Veritas, London-Based
Inchcape Testing Services International (ITSI), and Houston-based Inspectorate America.
2"Tax farming", consisting of trusting tax collection to private individuals allowed to
retain a percentage of tax revenue, was widespread among Europe's monarchies up to the
XVIIIth century. On this, see e.g. Stella (1993).
1
De Wulf, 2003).
In the absence of PSI, customs operations in developing countries have
been plagued by two problems. First, when collusive corruption between
customs administrations and importers is widespread (as it is in many of the
least developed countries), underinvoicing is neither reported nor corrected,
depriving cash-constrained governments of much-needed tax revenue. Sec-
ond, inefficient customs operations long clearance times and complicated
procedures act as dissipative trade barriers, i.e. barriers that raise the
cost of imports without generating revenue. Corruption and inefficiency are
often two faces of the same coin as customs officers deliberately obstruct
procedures in order to force traders to pay bribes. These are very serious
issues which help explain why countries having reformed their trade regime
but not their customs administration have sometimes failed to reap the full
benefits of trade liberalization. Faced with a lack of political will to imple-
ment effective customs reforms, the World Bank and other donor institutions
have sometimes recommended the outsourcing of customs operations to the
private sector with the objective of providing a parallel information system
that enables the government to control the tax collection functions of its own
burocracy (see Low, 1995).
Has PSI really helped mitigating the problems that prompted its use?
To our knowledge, there have been to date only two attempts at measur-
ing in a systematic way PSI's impact on collected tariff revenue. First, a
report by Argentina's Latin American Economic Research Foundation, com-
missioned in 1999 by SGS (FIEL 1999), compared the unit values of imports
into Argentina with unit values of similar goods destined to Chile. On the
2
assumption that Chilean customs are by and large uncorrupt, the discrep-
ancy between unit values was taken as a proxy for underinvoicing of ship-
ments to Argentina. FIEL found indeed that underinvoicing was curbed by
the introduction of PSI. One problem with FIEL's methodology is that the
introduction of PSI services may have been accompanied with other tariff
and/or customs reforms.3 Moreover, even if we fully attribute the decline in
underinvoicing to the introduction of PSI services, one may wonder whether
this decline was sufficiently large to compensate for the budgetary cost of
PSI (typically around one percent of imports; see next section).
More recently, Yang (2002) assessed the performance of the Philippines'
PSI program, taking advantage of its staggered implementation. As a pro-
gressively larger number of source countries were included, he showed that
imports covered by the program were increasingly diverted to tax-exempt
export processing zones, and from there illegally brought onto the domestic
market.4 Thus, in the presence of tax loopholes, PSI seemed to have affected
the form of fraud rather than its extent. Yang's results for the Philippines
were reinforced by panel estimation of a measure of underinvoicing (discussed
below) on tariff rates and a dummy variable equal to one for country/year
pairs with PSI programs in force. The PSI dummy was insignificant, sug-
gesting no statistically traceable effect of PSI on collected tariff revenue.
By its very nature, like all forms of fraud, tariff evasion cannot be mea-
sured directly, so roundabout methods must be used. The most common one
3Some have argued that a more uniform tariff structure may reduce tariff evasion; see
Gatti, 1999.
4Yang explains why such trade deflection did not take place before the program's in-
troduction by arguing that if PSI raises the variable cost of fraud while deflection to the
EPZ involves a fixed cost, PSI can make deflection attractive when it was not before.
3
consists of comparing the records of source and destination customs. Traders
attempting to evade import tariffs will underinvoice the value of shipments
to destination customs while no such incentive exists at origin ones. In the
presence of import-tariff evasion, discrepancies between source and destina-
tion trade data reported to Comtrade by national customs will thus reflect
not just CIF/FOB differences and measurement errors (on this, see De Wulf,
1981, or Feenstra and Hanson, 2000) but also the extent of deliberate under-
invoicing.
There are several potential problems with this method. One is that for
the very reason that they are primarily interested in collecting tariffs and ver-
ifying compliance with domestic regulations, customs monitor imports more
carefully than (if at all) exports. Thus, exports are subject to significant
measurement errors. However, exporters are legally liable for their declara-
tions to customs. If, upon audit by their home country's fiscal authorities
(say, for corporate profits tax verification), they were shown to have double
accounts, they would be in breach of tax laws. One may suppose that they
will avoid putting themselves in such a situation without a good reason to
do so.
Another problem is that, until all governments adopt the WTO's "trans-
action value" principle, idiosyncratic regulations may bias customs-recorded
values. For instance, until 1996 the Philippino government enforced a Home
Consumption Value (HCV) rule according to which imports into the Philip-
pines had to be valued at the exporting country's first-level-of-distribution
price. Thus, goods imported from, say, Switzerland and sold in the Philip-
pines at a fraction of their Swiss price had nevertheless to be reported at
4
their Swiss ex-factory price instead of at the transaction's actual price. The
HCV rule biased downward the degree of underinvoicing apparent in trade
statistics.5 None of these issues is serious enough to jettison the comparison-
of-trade-values method, but they suggest that care must be exercised in its
use.
Based on this method Fisman and Wei (2001) found that import-tariff
evasion between Hong-Kong and mainland China is significant, both through
underinvoicing and through (presumably deliberate) misclassification of im-
ports into tariff lines with lower rates. They also found a positive relationship
between tariff rates and underinvoicing.
If the idea that higher tariffs encourage fraud sounds plausible a priori,
the relationship may not, as a matter of fact, be so clear-cut. For instance,
categories of goods with high tariffs may be those most carefully scrutinized
by customs, so trying to fraud in those categories may be just the wrong
thing to do. Indeed, the relationship between tax rates and tax evasion can
theoretically go either way (see Slemrod and Yitshaki, 2000, for a survey).
In this paper, we first provide prima-facie evidence on the impact of PSI
on tariff evasion in different countries using nonparametric methods. For each
country and year, we derive kernel densities of the degree of underinvoicing
across tariff lines. We then retrieve cumulative distribution functions (CDF)
and propose a simple test: when the pre-PSI CDF of the underinvoicing
variable dominates the post-PSI one in the first order, PSI can be said to
have reduced underinvoicing.
5We are grateful to the SGS for providing this information. On this, see also Medalla
et al. (1993, 1999).
5
Second, we set up a simple game-theoretic model of tariff evasion and cus-
toms effort generating testable predictions about the relationship between
tariff rates and evasion. The model relies on an information-production
framework developed by Aghion and Tirole (1997) and applied to corrup-
tion problems by Anson (2003). The idea is essentially that customs must
spend costly resources assessing the value of shipments and that the outcome
of their effort is stochastic (that is, higher levels of effort only reduce the
likelihood of errors). This idea seems particularly well suited to a customs-
operation context where officers must determine how thoroughly they inspect
shipments knowing that exact valuation may be elusive even after careful in-
spection (especially for capital equipment which requires technical knowledge
to be properly valued). In this context, what PSI does is to provide addi-
tional information on shipment value. In a perfect world, this information
would only be used by the client government to control fraud. Alternatively,
if government authorities fail to use the information through audits and rec-
onciliation, it simply generates informational rents for corrupt customs officer
that they will share with importers through bribery arrangements.
Thus, with endogenous customs effort, importers deciding how much they
underinvoice must avoid attracting customs' curiosity, not so much because of
penalty tariffs but because uncovered fraud improves the bargaining position
of corrupt customs officers. The model shows that the introduction of PSI
services has an ambiguous impact on the extent of customs fraud. The model
also shows that irrespective of the presence of PSI, there tends to be less
underinvoicing in product categories with high tariff rates because those are
subject to more careful inspection and importers know it.
6
We test this prediction by structural estimation of the model's first-order
condition on panels of disaggregated imports for several countries and years
and find that indeed, underinvoicing is inversely related to tariff rates. Our
estimates also suggest that the extent of fraud might increase or decrease
after PSI's introduction.
The paper is organized as follows. Section 2 briefly describes PSI proce-
dures. Section 3 presents nonparametric test results for a sample of countries.
Section 4 sets out the model, and section 5 presents the econometric analysis
and results. Section 6 concludes.
2 PSI procedures
Import procedures under PSI vary, but the typical one is roughly as follows.6
The trader operating in the port of shipment must first provide the PSI
company's local agent with a detailed description of the shipment, which
is then inspected. Upon inspection, the PSI company issues a Report of
Findings, which falls into two categories: a Clean Report of Finding (CRF),
when the PSI company confirms the trader's declaration or a Discrepancy
Report (DR) when the PSI uplifts the value declared by the trader. The
CRF or DR serves as a basis for the determination of applicable import-
tax regime (tariff line, special regimes, exemptions etc...) and is sent to the
destination port's customs and PSI company agent. In addition, it is also sent
for reconciliation purposes to the client government's Ministry of Finance;
the extent of reconciliation between customs data and the CRF/DR by the
6For a more detailed description, see Low (1995), page 9.
7
Ministry of Finance varies across countries, but the reconciliation rates tend
to be low.
At the destination port, the importer or a registered commissioner for-
wards one copy of the report to the appropriate customs office, together with
a set of official customs documents on the basis of which duties payable are
assessed. On the basis of these two sets of documents (CRF/DR and customs
documents) the PSI company calculates all taxes and duties, which are paid
by the importer or commissioner to a designated bank account, from which
they are transferred to the Customs' account at the Central Bank and then
finally to the Treasury. To these duties, the PSI company adds a fee paid
by the importer, typically about 1% with a minimum amount.7 Shipments
landing at the port of destination without having been inspected at the port
of embarkation are liable to destination inspection, with penalties for repeat
offenses (typically, additional taxes on the second occurrence and seizure
thereafter). Customs also sometimes perform independent inspections (in
addition to PSI).
Disputes between importers and the PSI companies should in principle be
settled by an arbitration body, but few PSI-using countries have set up such
bodies. In their absence, importers have no recourse in case of dispute with
the PSI company beyond the right to a second inspection, usually performed
in the 48 hours following the complaint.
7For instance, in a number of countries, SGS charges 1.05% of shipment value over
a de minimis threshold of $5,000 with a minimum fee of SFr 450 (around $300). For
small shipments, this may add substantially to the burden of import tariffs (a $300 fee
on a $5,000 shipment represents an ad-valorem equivalent of 6.15%) and this may have
non-negligeable effects in LDCs (least developed countries) where median shipment size is
small. See WTO (1999).
8
3 PSI and underinvoicing: prima-facie evi-
dence
This section provides evidence on tariff evasion before and after the introduc-
tion of PSI services for a subsample of 16 countries, for which trade data was
available during a sufficient number of periods preceding and following the
introduction of PSI, among a set of 52 countries that have used PSI services
at some point in time.8 The method used here is based on a comparison
between the trade statistics of source and destination countries at the tariff-
line level. In the absence of fraud, source and destination flows should be
identical up to measurement errors and the difference between CIF and FOB
valuations. Thus, the density function of the differences between the depar-
ture and arrival records should closely resemble a normal density centered
around the CIF-FOB difference. Irregularities or `thick tails' can reflect two
economic forces, noted in the introduction: underinvoicing meant to avoid
import duties, or overinvoicing meant to evade capital controls or local taxes.
In order to measure the extent of tariff evasion, we look at bilateral export
flows from the EU to all countries having used PSI services, taking export
values reported by EU customs shipments' true values (call it V ) and import
values reported by destination countries as underinvoiced values (v). We
then estimate, using the Kernel method, the weighted9 density function of
the ratio (V - v)/V averaged over 5 years preceding and following the
8The 16 countries correspond to the number of countries for which we have trade data
available before and after the introduction of PSI services. The econometric results in the
next section are only give for 3 of these sixteen countries, for which we also had tariff data
before and after the introduction of PSI services.
9Weighted by a measure of the volume of trade.
9
introduction of PSI.
Figure 1 plots the difference between EU-Switzerland bilateral flows recorded
by source and destination customs, in value. The density, while perhaps more
easily approximated by a double exponential density than by a normal one,
is indeed symmetric and regular.
By contrast, comparable densities for developing countries (three of which
are reported in Figures 2-7)10 are highly irregular and suggest that more
than measurement errors are at work. For those, evidence of underinvoicing
largely dominates evidence of overinvoicing, as the distributions tend to be
skewed to the right indicating that in a large number of transactions the
value declared at the importing country is smaller than the value declared at
the embarkation port. This is consistent with the fact that capital controls
have largely been phased out.
In order to get a more precise estimate of the shift in underinvoicing
frequencies, Table 1 shows the probability that the true value is larger than
the declared import value before and after the introduction of the PSI in
each of those three countries. It also shows the probability that the ratio
takes a value in the right-hand tail11 of the distribution, i.e. the likelihood
of observing signficant levels of underinvoicing (both in terms of value and
quantity).
A sharper test is based on the notion of first-order stochastic dominance.
Consider two cumulative distribution functions F1 and F2, both defined on
10These are the three countries for which we also have tariff data before and after the
introduction of PSI services and that we therefore use in our econometric analysis in the
next section.
11Deviations higher than 80 %.
10
R. F1 is said to dominate F2 in the first order if
F1(x) < F2(x) x R.
The relationship between F1 and F2 and their respective densities f1 and f2
is shown in Figure 8. In Figure 1 F1 stochastically dominates F2 in the first
order, as it always lies below F2, indicating that the probability of x being
larger than a certain number is always larger when the distribution takes the
form of f1.
Intuitively, first-order stochastic dominance describes a shift to the right
of the density function such that the CDF's never cross. In our context,
a shift to the right corresponds to more fraud. Therefore we can say that
PSI is unambiguously successful if the pre-PSI distribution of dominates
its post-PSI distribution in the first order. The test does not require any
assumption about the relevant distributions (which the kernel technique does
not characterize mathematically) but simply a plot of the relevant CDFs. By
this test, the introduction of PSI was a success in six out of sixteen countries
for which we have data available (Indonesia, Kenya, Mozambique, Niger,
Senegal and Togo). It was a failure in two (Ecuador, and Madagascar); and
the test is inconclusive for eight others (Argentina, Bolivia, Ghana, Guinee,
Malawi, Mali, Peru and the Philippines). Figures 9-11 below show the kernel
density and CDF estimates for three countries for which we will also report
econometric results later on in this paper: Argentina, Indonesia, and the
Philippines.
As mentioned above, and as can be seen from Figures 9-11, only Indone-
sia's CDFs represent an a priori clear-cut case in favour of PSI, since CDF
11
curves before and after the introduction of PSI do not cross, and correspond
to a displacement from the right (without PSI) to the left (with PSI). More
interestingly, Indonesia's case is confirmed as an a priori success of PSI re-
gardless of whether we choose the years preceding the introduction of PSI12
(1985) or those following the withdrawal of the program13 (1997) to conduct
the " with and without " analysis. In each case, the extent of fraud appears
to be lower in the presence of PSI, an evidence which is both confirmed by
the PSI company itself (SGS) and the recent complaints of the Indonesian
private sector on customs behavior. Note that these results are robust to the
type of trade data used, i.e. values or quantities. Yet whether this seemingly
lower level of fraud is related to pure PSI effects still remain to be confirmed
by a further theoretical approach and its proper econometric testing, enabling
to disentangle between what is really due to PSI and what was the result of
other factors.
As for Argentina, CDFs curves cross both at the lower and upper tails of
the distribution, suggesting a worsening of extreme deviations cases in the
presence of PSI. Since a conclusion cannot be drawn a priori in the Argen-
tinian case, the evaluation of PSI efficiency for reducing fraud is entirely left
to the approach which is developed in the next two sections. The Philip-
pines CDFs do not provide an unambiguous answer either. Finally note that
the CDFs curves, whether crossing or not, are rather close from each other,
12The years used to build the Kernel densities are then 1980, 1981, 1982, 1983 and 1984
for the " without PSI " density curve, and, 1985, 1986, 1987, 1988 and 1989 for the " with
PSI " density curve.
13The years used to build the Kernel densities are then 1997, 1998, 1999, 2000 and 2001
for the " without PSI " density curve, and, 1992, 1993, 1994, 1995 and 1996 for the " with
PSI " density curve.
12
which The a priori suggests that the introduction of PSI had a weak impact
on customs fraud.
The first-order dominance test, however, is both too strong and not
enough. It is too strong in the sense that any crossing of the CDFs is
enough to reject the hypothesis that fraud was reduced, even if this crossing
is due to an irregularity in the density function (potentially itself the result
of measurement errors). At the same time, it is not strong enough in that
any arbitrarily small translation of the same distribution along the real axis
qualifies as dominance. Therefore we turn now to a more formal approach.
4 Underinvoicing: an analytical setup
We explore the issues described above through a simple model featuring two
components. First, a "positive" (i.e. descriptive) component sets out the
strategic interaction between two classes of agents, importers and customs.
The environment in which these agents make decisions (declared value for
importers, inspection intensity for customs) is potentially affected by the
presence and efficiency of a PSI company. Timing and information are speci-
fied precisely through the use of an extensive-form game. Second, a "norma-
tive" (i.e. policy choice) component features two types of control variables at
the government's disposal: internal-incentive variables (bonuses to customs
officers for fraud catches and sanctions for uncovered collusion with fraud-
ing importers) and external-incentive ones (intensity of use of PSI-provided
information through reconciliation of customs and PSI data). The use of ex-
ternal (PSI-supplied) information acts as an incentive device provided that
13
it is common knowledge, because it affects the effort and collusion decisions
of customs through the probability of being caught.14 Both importers and
customs are assumed purely opportunistic, which means that importers min-
imize tariff payments while customs maximize bribe and bonus income net of
expected sanctions and the disutility of effort. Ethical considerations could
be added easily to the objective function of customs but would add little to
the analysis.15
We focus on a single transaction, for which the sequence of events is as
follows. An importer chooses the declared value v of a shipment worth V
on which a tariff is applicable at ad-valorem rate t. V is known only to
the importer.16 At the port of embarkation, a PSI company inspects the
shipment and reports its own estimate of shipment value in documentation
sent to the destination port's customs, together with the importer's initial
declaration. To fix ideas, think of the good being shipped as a piece of
machinery whose valuation requires technical knowledge. With probability
p, the PSI company possesses or acquires the required technical information
and is able to value the shipment correctly at V . With probability 1 - p,
it fails and simply reports the importer's declared value v. We will treat p,
which can be thought of as the PSI company's reliability, as a parameter.
The next stage takes place at the destination port's customs where the
shipment and accompanying documentation are inspected.17 Prior to inspec-
14 We abstract from outright smuggling which entirely bypasses customs clearance and
for which pre-shipment inspection provides no solution.
15 This also implies that we have very little to say regarding the welfare of customs
officers in different equilibrium.
16 Focusing on a single transactions allows us to ignore shipment size issues, so V can be
thought of as either total or unit value.
17 In principle, shipments subject to PSI are not liable to second inspection by destination
14
tion, shipment value is considered by customs as a random variable V . The
(subjective) prior distribution of V does not need to be specified in what
follows. Customs observe two signals on the basis of which they can update
their prior: one from the importer and one from the PSI company. The pair
of valuations provided in the two documents (importer declaration first, PSI
document second) is either (v, V ) or (v, v). In the former case, which occurs
with probability p,18 customs obtain the correct valuation directly from the
PSI company. In the latter, which occurs with probability 1 - p, they infer
that the PSI company is simply reporting the importer's declaration which,
in an interior equilibrium, they know to be wrong.19 In that case they under-
take inspection.20 The surprising notion that customs undertake inspection
only when PSI documents and importer declaration match comes from the
fact that the importer's initial declaration to the PSI company is also sent to
customs with the CRF or DR with no possibility for opportunistic revision.21
customs upon landing. Practices vary widely across countries, with `second-inspection'
rates ranging from 5% for some countries to 100% for others (e.g. Nigeria). There is no
overall statistics on the rate of second inspection but a surveillance company estimates it
at around 40% of shipments worldwide.
18As a simplification, we assume that p is the PSI company's probability of finding
the shipment's true value whether the importer declared truthfully or not. Letting the
PSI company update its beliefs using v would complicate the model's description without
affecting its results.
19As will later become clearer, for some paramater values, it is possible to construct a
"no-fraud" equilibrium assessment (set of strategies and beliefs) in which importers never
fraud (v = V ) and customs beliefs are consistent with this. We will henceforth disregard
this case, although it may of course occur in reality.
20Instead of being assumed, the situation in which customs do not perform second
inspections at the destination port emerges endogenously as the equilibrium outcome when
p = 1 (see below).
21If it could be revised, then each time the PSI company followed the importer's initial
declaration, the importer would underdeclare even further at customs in order to create
the illusion that the PSI's higher valuation was the correct one. Customs' beliefs would
therefore need to take account of this strategic behaviour.
15
Let inspection intensity (effort) be measured by a continuous variable e
[0, 1] with quadratic effort cost c(e) = e2/2. Quadratic effort cost guarantees
a closed-form solution. As in Aghion-Tirole, we will interpret e both as
a measure of customs effort and as the (endogenous) probability that the
valuation obtained is correct. When the valuation is correct, customs know
that it is so. The assumption is that the information can be readily verified.
Failing to produce the information, customs can only use v as a signal to
update their beliefs about shipment value. Even if they know, because the
game's parameters are common knowledge, that importers always underin-
voice in equilibrium, customs have in this case no verifiable information to
support a fraud claim. In order to avoid introducing an element of arbitrari-
ness in the model, we will then suppose that no fraud claim can be made, so
that customs' beliefs are, in this particular instance, inconsequential.
Knowing customs' information set, the importer decides on a bribe of-
fer expressed as a fraction of fraud value, which customs can accept or
reject. Finally, the government reconciles through random audits the infor-
mation provided by PSI and customs. Audit probability is and is a policy
variable.22 Fraud, whether uncovered through audit or through customs re-
ports, is met with a punitive tariff surcharge at ad-valorem rate T. Customs'
"catches" are rewarded with a bonus b expressed as a fraction of tariff rev-
enue recovered,23 whereas cases of collusion between customs and frauding
22Reconciliation between PSI- and customs-provided information is very irregular. A
surveillance company estimates the reconciliation ratio at around one third of all transac-
tions subjected to PSI.
23In practice, rewarding customs officers with a percentage of catches is relatively un-
common. Incentive systems are however increasingly introduced as part of customs reform
package and often include staff funds rather than individual rewards. There is no database
16
importers are met with sanctions on customs officers. Those sanctions are
assumed to have the form
k = k0 + k1(V - v)t
i.e. including a constant and an amount proportional to the uncovered fraud.
These two components are unlikely to be there simultaneously but their in-
clusion in the formulation makes it possible to explore two alternative inter-
pretations: when k1 = 0 the penalty is fixed (say, the officer is fired), whereas
when k0 = 0 the penalty is a fine or sanction (say, suspension without salary)
proportional to the severity of the offense. The game is solved backwards.
4.1 Equilibrium
4.1.1 Rent-sharing in collusive equilibria
In the last stage of the game, customs, faced with a bribe offer , decide
to accept it or not. The information available to customs is a triplet I =
(I, P, C) describing, in this order, the importer's declaration I, the PSI's
valuation P, and customs' own valuation C. If any one of I's three elements
is V , customs knows the shipment's true value with certainty and it knows
that it knows. Let x {1,0} be the customs' decision decision to accept the
bribe or not, with the convention that x = 1 means acceptance. Three cases
must be considered.
Suppose first that the PSI company succeeds in valuing the shipment
comparing such incentive schemes but a customs analyst interviewed for this paper put
the most common bonus rate at around 20% of the value of catches.
17
correctly (P = V ). The state of information is IP = (v, V, .). Knowing
shipment value, customs considers inspection unnecessary and sets e = 0.
Accepting a bribe offer is risky because it could be uncovered through rec-
onciliation of PSI and customs-provided documents; alternatively, reporting
the discrepancy and charging the importer accordingly does not buy customs
officers any bonus since the "catch" is really the surveillance firm's.24 Thus,
customs' expected utility given the state of information is:
u(x; IP) = ( - k1) (V - v)t - k0 if x = 1
0 if x = 0.
This defines the customs' participation constraint, i.e. the minimum bribe
that customs can accept given the risk of detection. The importer sets
so as to satisfy the constraint exactly, i.e. to leave customs just indifferent
between accepting and not. The bribe is then always accepted, under the
usual assumption that a binding participation constraint makes the contract
acceptable. Solving and rearranging gives
k0
P = k1 + (1)
(V - v)t
where the subscript means that P is the bribe offered when the shipment's
value has been reassessed by the PSI company.
Next, suppose that the PSI company does not correct the value of the
shipment (i.e., issues a CRF), reporting instead P = v. Then two cases
arise, depending on whether customs is successful or not in its own valuation
24 Adding a bonus when x = 0 does not alter the results qualitatively.
18
effort. If it is, the state of information is IC = (v,v, V ). The importer offers
again a bribe , although at a different rate. Because PSI documents create
no risk of `hostile' reconciliation by the government, collusion is now risk-free
for customs and
u(x; IC) = (V - v)t if x = 1
so the bribe offer is now C = b25 b(V - v)t if x = 0,
.
Finally, if customs is unsuccessful in its own valuation effort, the state of
information is II = (v, v,v); no credible threat of fraud claim can be made.
Thus
u(x; II) = (V - v)t if x = 1
0 if x = 0,
which gives I = 0 (no bribe).
4.1.2 Customs Inspection intensity
In our model, inspection takes place only when documentation provided by
the PSI company is deemed uninformative by customs. In that case, ex ante,
V is a random variable V with expectation E(V ) and the inspection-intensity
problem is:
e2 e2
max eC E V = eb E V
e - v t - 2 - v t - 2
25 Thus, increasing the bonus for catching fraud increases the bargaining power of the
customs officer when facing the bribing importer.
19
which gives
e(v) = b E V - v t. (2)
Thus, equilibrium inspection intensity is increasing in the government-provided
bonus b, in the tariff rate t, and in the level of fraud. Note that inspection is
undertaken by customs only when the PSI valuations are considered uninfor-
mative because identical with importer-provided declarations. Thus, average
inspection intensity is
E[e(v)] = (1 - p)b E V - v t, (3)
which decreases with the efficiency of the PSI company. In other words, PSI
efficiency is a strategic substitute for customs effort. Thus, the situation in
which PSI operates smoothly at the embarkation port and customs never
re-inspects at the destination port is the endogenous outcome of the model
(rather than assumed) when p = 1.
4.1.3 Equilibrium declaration
From now on, we will suppose that customs' (subjective) distribution for
V is centered on the shipment's true value, so E V = V , and that this is
known to the importer (but not to customs itself).26 The importer's problem
is to choose the declared value that minimizes the sum of duty payments and
26If customs knew what distribution V is drawn from and that this distribution is cen-
tered on V , they could infer V and the information-production problem would disappear.
20
expected penalties given equilibrium play in all subgames, that is,
min p [P(V - v)t + (1 - )vt + V (t + T)]
v
+(1 - p) [vt + eC(V - v)t]
s.t.
k
P = ,
(V - v)t
C = b,
e = b (V - v) t.
The maximand has the following interpretation. Either the shipment's value
is reassessed by the PSI company (an event with probability p) or not. If
yes, upon arrival a bribe P is paid to customs no matter what. If collusion
with customs is uncovered by reconciliation (an event with probability ),
the duty paid is V (t + T) i.e. includes a penalty rate and is applied on the
true value V . If not, duty paid is vt. If no reassessment, customs undertake
inspection with intensity e. Duty is paid on the declared value v no matter
what. If inspection is successful (an event with probability e), in addition a
bribe is paid at rate C.
Without the constraints, the importer's problem would always yield a
corner solution since the cost function to be minimized is linear in v. Thus
interior solutions (partial fraud) come from the importer's recognition that
a low declared value triggers more careful inspection.27
27As V is unkown, a lower v triggers more careful inspection not because it is suspect,
but because the expected return to inspection is an increasing function of E V - v no
matter what the distribution of V is.
21
Let = V - v be the degree of fraud. Expressed in terms of , the first
order condition is:
1 1 - 1p- + k1)
(1
= . (4)
2b2t p
It is easily verified that the game without PSI is outcome-equivalent to a
game with PSI but with p = 0. Letting
1 - 1p- + k1),
(1
(5)
p
we have thus
/2b2t with PSI,
= (6)
We have refrained from usingKuhn-Tucker conditions for ease of notation
1/2b2t without.
but it should be clear that corner solutions can be obtained at = V (total
fraud, which can be thought of as smuggling) when is large enough, or
at = 0 when < 0. In the latter case fraud is entirely eliminated by the
introduction of PSI. Two points are worth noting. First, unlike what has
often been suggested (Goorman and De Wulf, 2003 and Low, 1995), perfect
reconciliation (i.e., = 1 does not necessarily lead to the elimination of
customs fraud ( = 0) if the PSI company is not very efficient (p << 1) (and
the proportional part of the penalty is not very large, i.e., k1 0). A fuller
discussion of the effect of introducing PSI is differed until the next section.
22
4.2 Comparative statics
The model generates both positive and normative results which can be de-
rived as comparative-statics properties. As for positive results, the first and
most surprisingly is that fraud declines with the tariff for a wide range of
parameter values. This surprising result, which stands in contrast with the
findings of Fisman and Wei (2001), is due to the strategic interaction between
importer and customs. With collusive rent-sharing, a higher tariff raises
customs' incentive to find verifiable evidence of fraud, since such evidence
improves customs' bargaining position (more exactly its participation con-
straint). This strategic effect reduces the importer's fraud rent and swamps
the direct effect that a higher tariff exerts on the return to fraud, reducing
its equilibrium level.28 Because the inverse relationship between and t is
somewhat counterintuitive, it provides a test of the model's validity as a
descriptive tool.
As for normative results, raising the power of incentives facing customs
through an increase in the bonus rate b reduces the equilibrium level of fraud,
an intuitive result since fraud is encouraged by collusion with customs. So
does raising the frequency of audits () and the rate of sanctions.
By (6), the introduction of PSI reduces the degree of fraud if and only if
< 1, i.e. if (1 + k1) > 1. The model highlights the interdependence of PSI
28That the indirect effects (through customs' effort) always swamps the direct effect
(through fraud revenue) may seem surprising, but recall that without the indirect effect
the problem admits only corner solutions because the importer's minimand is linear in
t. The fact that fraud is observed and is less than one hundred percent suggests, in
this model's logic, that the desire to avoid attracting customs attention through gross
underinvoicing is indeed a key consideration (in accordance with intuition). The inverse
relationship with t then follows directly from the algebra.
23
efficiency (p) and reconciliation rates () in curbing fraud. Differentiating
(5) with respect to p at the two extreme values of gives
= 1 - (1 + k1) =
It can be shown that there is a singlepoint where /p changes sign. Thus,
p (1 - p)2 -k1/(1 - p)2 if = 1 (7)
1/ (1 - p)2 if = 0.
more efficient PSI (a higher p) reduces fraud only when the rate of recon-
ciliation () is high enough. When = p = 1, is negative and a corner
solution is obtained at = 0 (no fraud). It can be also seen that when is
high enough to make /p negative (upper part of 7) the latter goes up in
absolute value with increases in k1, the rate of sanctions on customs officers.
This set of results highlights the complementarity of PSI with government
efforts to fight customs corruption through internal incentives (k1) and to
make use of PSI information ().
The intuition of the case in which the introduction of PSI ends up raising
fraud is as follows. When fraud is uncovered through PSI (case IP) the
bargaining position of corrupt customs is weak due to the fact that reporting
the fraud brings no bonus. Therefore the informational rent generated by
PSI is entirely captured by the importer, which raises the return to fraud.
There is then more fraud in equilibrium. Introducing a bonus for when
customs officers report fraud uncovered by PSI or letting the rent be shared
by the Nash bargaining solution would weaken this mechanism but would not
necessarily reverse it.29 Thus, in general whether PSI reduces tariff evasion
is an empirical question.
29For instance, introducing a bonus at rate b1 for customs officers using PSI data to
24
In models of information production in which efforts are strategic sub-
stitutes, the arrival of an additional information-producing agent can either
raise or lower aggregate information production, depending on whether the
agent's direct contribution to aggregate effort offsets or not the negative ef-
fect of her arrival on the marginal effort of other agents. Here, customs effort
is indeed decreasing in the PSI company's efficiency, as E(e) is a decreasing
function of p (see (3)). However aggregate information production neces-
sarily goes up with the introduction of PSI. To see this, define to be the
probability that the shipment's true value is established by either customs
or the PSI firm. With PSI,
= p + e(1 - p)
= p + (1 - p)b(V - v)t
using (2). Without PSI, customs' effort is still given by (2), so
= b(V - v)t.
report fraud would change (7) into
if = 1
= 1 - [b1 + (1 + k1)] (
= 1 /(1 - p)2
p (1 - p)2 -(1b1-+b1k)/)(1- p)2 if = 0.
Obviously, qualitative results would not change as long as the bonus rate is less than one
(which it realistically has to be), but increases in p would have a stronger effect when is
high enough.
25
It is easily seen that
- = p[1 - b(V - v)t]
= p [1 - e(v)] > 0
where the last inequality follows from the fact that e is a probability. The
reason for this result is that information production is here sequential in-
stead of simultaneous, as it is in Aghion-Tirole or Anson. Once PSI has
been observed to fail, customs face essentially the same problem that they
would without PSI, so they do not free-ride on PSI effort. This means that
information-production efforts are additive.
In sum, the introduction of PSI unambiguously improves the state of
information. However, its effect on fraud is only indirect, and the model's
answer to the question `does PSI help?' is reflected in the slope difference
between the upper and lower parts of (6). We now turn to an empirical test
of the model's predictions.
5 Econometric estimation
This section presents an attempt to estimate structurally first-order condition
(6) on panels of imports from the EU, disaggregated at the SITC2 5 digit
level for PSI-using countries. The initial sample included 52 countries. Of
those, 16 had disaggregated trade data for a sufficient number of years before
the introduction of a PSI program and a sufficient number of years after.
Among those 16, 6 had tariff data as well, but only 3 for years preceding and
following the introduction of PSI (i.e. Argentina, Philippines and Indonesia).
26
Thus, the final sample has 3 countries, each with between 5,799 and 7,019
observations (tariff lines at the SITC 5 digit level). Trade data is from the
UN's Comtrade database and tariff data from UNCTAD's Trains.
5.1 Procedure
The equation to be tested is a stochastic version of equation (6) estimated by
country after pooling pre- and post-PSI years respectively. As heteroskedas-
ticity is likely to be an issue, Eicker-White heteroskedasticity consistent es-
timators are provided. We will thus be able, without specifying the type of
heteroskedasticity, to make valid inferences based on the results of ordinary
least squares. In order to avoid having V on both the RHS and LHS, we
rewrite (6) as
v(V, t) = V - /2b2t with PSI,
V - 1/2b2t without.
Although the model has no constant, we add time effects to pick up the
influence of out-of-model changes in the environment. The effect of tariff
changes and customs reforms involving changes in incentive structures should
be picked up by parameter estimates, but other changes in the environment
need to be controlled for.
In order to account for positive deviations of v from V (those are aber-
rations in the model but nevertheless present in the sample) we interact
1/t with a dummy variable z equal to one when v < V (the normal case).
Although several approaches are possible to deal with this problem, none
yielded drastically different results and we view this one as a better alter-
native than dropping altogether the "problem" lines, which would bias the
27
sample.30 Finally, the dummy variable is equal to one in PSI years and zero
otherwise. PSI years are 1998-2000 for Argentina, 1993-1995 and 1998-2000
for the Philippines, and 1989-90, 1993, 1995-6 for Indonesia. The holes in
PSI years for Indonesia and the Philippines are years without tariff data.
Letting subscripts i and k refer respectively to periods and commodities,
the transformed structural equation to be estimated is:
T
ziki
vik = 0idi + 1Vik + 2 + 3 zik(1 - i) + ik (8)
tik tik
i=1
where ik is an error term. Note that source custom values are FOB whereas
destination values are CIF, so in order to interpret the former as true values
and the latter as `underinvoiced' values, the CIF/FOB difference must be
taken into account.
The model's predictions are 1 = > 1, where is the CIF/FOB ratio,
2 = -/2b2 < 0, and 3 = -1/2b2 < 0. Some of the model's structural
parameters can be retrieved from the estimates. For instance, b = 1/23
and = 2/3. Using an interview-provided "guesstimate" of equal to 0.3
(see supra), the implied estimates for and b can be used to get one for p
under different hypotheses for k1.
5.2 Results
Robust regression results are shown for Argentina, the Philippines and In-
donesia (with numbers of observations ranging between 5, 799 and 7, 019 for
30Our method implies that the influence of observations with v > V is picked up by the
constants (year effects) and the error term, which is appropriate if those observations are
thought of as measurement errors.
28
each regression) in Table 2. As predicted by the model, for all countries
the coefficient on 1/tik is negative31 (recall that the dependent variable is
v rather than the degree of fraud) and always significant at the 1% level.
2 ranges across regressions between -25,076 (for Argentina) and -10,752
(for Indonesia); 3 ranges between -15, 824 (Philippines) and -8,218 (Ar-
gentina).
One of the model's implications is that PSI reduces fraud when is
smaller than one. As = 2/3, we have
= 30..051 for Argentina,
585 for the Philippines,
1.257 for Indonesia.
Thus, the point estimates suggests that customs fraud has increases with
the introduction of PSI services in Argentina and Indonesia. Testing the
null hypothesis that = 1 (no effect for PSI) gives Wald test statistics of
F(1, 5893) = 56.74 for Argentina, F(1, 7006) = 7.28 for the Philippines, and
F(1, 5789) = 1.02 for Indonesia. The null hypothesis is accepted for Indone-
sia, for which PSI appears to have had no traceable effect, but rejected for the
other two countries. In the Philippines, PSI helped, whereas in Argentina, it
seems to have made things worse.32
Implied estimates of b (the bonus rate for catches, a proxy for inter-
31We also estimated the model by country and year, and got a significant negative
coefficient on 1/tk in 47 regressions out of 49.
32Note that our estimation does not control for evasion of customs tariffs through the
more intese use of duty free zones, which Yang (2003) suggest were an importance force
in evading customs tariffs in the Phillipines after the introduction of PSI services. Taking
this account may weakened even further the case for PSI services.
29
nal incentives in customs administrations) are b = 0.00780 for Argentina,
b = 0.00562 for the Philippines and b = 0.00765 for Indonesia, suggesting
very weak incentives. These low estimates are in accordance with anecdo-
tal evidence. Substituting estimated values for b and using = 0.3 gives
estimates of p (the frequency of catches by PSI firms) depending on k1. For
Argentina, for instance, we get p(0) = 0.745 and limk1 p = 1. For the
Philippines, we get p(2.3) = 1 and limk1 p = 0 (k1 cannot be lower than
2.3 when is less than one). The fact that implied estimates of p are between
zero and one is consistent with the model where p is a probability.
Finally, 1 provides an estimate of CIF/FOB ratios equal to 0.987 for
Argentina, 1.329 for the Philippines and 1.150 for Indonesia. The estimate
for Argentina is clearly biased downward, but the upper bound of the 95 %
confidence interval (equal to 1.03675) is nevertheless above unity. The other
two estimates are plausible. In sum, most estimates of the model's para-
meters, direct or implied, are in plausible ranges, vindicating the approach
taken in section 4.
6 Concluding Remarks
This paper attacked the title's question (`does PSI help reducing tariff eva-
sion?') from two perspectives. First, we showed prima-facie evidence based
on non-parametric methods suggesting a mixed picture, with some cases of
unambiguous reductions in evasion and others suggesting no improvement.
The problem with this approach is that it does not control for other tariff
and customs reforms that may have occurred simultaneously when trying to
30
evaluate the impact of the introduction of PSI services in client countries.
The second approach corrects for this and uses a structural model. We
derived a simple game-theoretic setup with strategic interaction between im-
porters' fraud decisions and customs' effort. The model has positive and
normative implications. It highlights that importers understand that cus-
toms have a sharper eye on high-rate tariff lines, making fraud trickier (if
potentially more lucrative) in those lines. Denunciation fears act only as
off-equilibrium threats, the equilibrium being generally one with collusion
between frauders and corrupt customs. Based on relatively straightforward
strategic interaction, the model predicts less fraud in tariff lines with high
rates (because those are the ones on which customs focus their attention).
This counterintuitive prediction provides a test of the model against the
traditional, intuitive approach that higher tariff rates encourage fraud. Per-
haps more importantly, the model suggests that PSI's impact on the extent
of fraud is theoretically ambiguous. The reason is, intuitively, that PSI pro-
duces information which is only worth what the client government authorities
decide to do with it. PSI may even have a perverse effect in de`-motivating'
customs. This effect appears indirectly in our model through the following
mechanism. When reporting fraud uncovered by PSI, customs officers do
not expect to receive bonuses (as opposed to when they uncover fraud them-
selves). Their only motivation to report PSI data and force importers to pay
penalty duties is the threat of sanctions if data is later reconciled. When the
frequency of reconciliation is low (as it typically is) that incentive is weak.
This, in turn, creates a situation where collusion between frauding importers
and customs is likely. At the same time, the weakness of customs' incen-
31
tive to report affects out-of-equilibrium payoffs in a way that strengthens
the bargaining position of importers, raising the equilibrium return to fraud
and, consequently, the incentive to fraud. If the chain of incentive effects
just described may seem somewhat indirect, its final outcome (demobilized
customs) has been widely observed in countries adopting PSI (Low, 1995 and
Goorman and De Wulf, 2003).
Finally, we tested the model on panels of imports between the EU and
PSI-using countries at a high degree of disaggregation and found that its ba-
sic prediction (fraud being inversely related to tariff rates) was strongly sup-
ported by the data. Structural parameter estimates are in plausible ranges,
giving support to our modeling approach. Finally, econometric results for the
three countries for which we have tariff and trade data before and after PSI
suggest that the introduction of PSI in those countries led to an increase in
the extent of fraud in Argentina, lending support to the model's claim that
indirect (incentive) effects can dominate direct (information-production) ef-
fects, and was clearly successful only in the Philippines. Indonesia appears
as a mixed case.
References
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in Organizations"; Journal of Political Economy 105, 1-29.
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32
[3] Byrne, Peter (1995), "An Overview of Privatization in the Area of Tax
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[4] De Wulf, Luc (1981), "Statistical Analysis of Under- and Overinvoicing
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attention for developing countries", mimeo, The World Bank.
33
[11] Johnson, Noel (2001) "Committing to Civil Service Reform: The
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Valuation: A Policy Paper"; PhilExport/USAID.
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[16] Slemrod, Joel, and Shlomo Yitzhaki (2000), "Tax Avoidance, Evasion,
and Administration"; NBER working paper 7473.
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Reform"; mimeo, Harvard.
34
Table 1: Tariff evasion before and after PSI
Country Values Quantities
Pr( > 0) Pr( > 0.8) Pr( > 0) Pr( > 0.8)
Indonesia (.55, .63) (.10, .17) (.58, .61) (.08, .14)
Philippines (.69, .68) (.15, .10) (.57, .62) (.13, .09)
Argentina (.62, .51) (.03, .03) (.71, .61) (.04, .07)
Note: Values reported in parentheses: without PSI first, with PSI second.
35
Table 2: Estimation Results
Variable Argentina Philippines Indonesia
Vik 0.987 1.329 1.150
(0.026) (0.197) (0.099)
(ziki)/tik -25076.45 -9260.48 -10752.15
(1791.95) (2137.09) (1720.86)
(zik(1 - i))/tik -8218.49 -15823.84 -8553.79
(1348.83) (2173.71) (1613.14)
d1988 332.75
(191.18)
d1989 180.70 775.36
(191.60) (170.04)
d1990 650.28 690.50
(270.19) (238.19)
d1991
d1992 103.24
(244.33)
d1993 -89.60 1469.34
(198.28) (354.06)
d1994 297.05
(241.22)
d1995 593.02 198.68 907.71
(134.71) (283.99) (329.27)
d1996 563.64 1240.62
(151.09) (306.21)
d1997 808.95
(170.37)
d1998 1640.14 869.10
(173.02) (337.13)
d1999 1658.94 1148.22 818.70
(151.59) (471.20) (218.19)
d2000 1503.14 1125.06 645.19
(131.18) (611.32) (204.20)
Number of observations 5902 7019 5799
Adjusted R2 0.8716 0.2984 0.7027
F-Stat 646.88 103.06 282.05
Note: standard error of coefficient between parenthesis
36
Figure 1: Switzerland's Kernel Density
2.16625
9991vfx
.016779
-1 0 1
devvalue
Kernel Density Estimate
37
Figure 2: Kernel Density For Value Deviations (Argentina)
density: devvalue_without density: devvalue_with
1.37561
0
-1 0 1
value_deviation
Argentina
Figure 3: Kernel Density For Quantity Deviations (Argentina)
density: devqty_without density: devqty_with
1.46307
0
-1 0 1
quantity_deviation
Argentina
38
Figure 4: Kernel Density for Value Deviations (Philippines)
density: devvalue_without density: devvalue_with
.922202
0
-1 0 1
value_deviation
Phillipines
Figure 5: Kernel Density For Quantity Deviations (Philippines)
density: devqty_without density: devqty_with
1.0141
0
-1 0 1
quantity_deviation
Philippines
39
Figure 6: Kernel Density for Value Deviations (Indonesia)
density: devvalue_without density: devvalue_with
.924511
0
-1 0 1
value_deviation
Indonesia
Figure 7: Kernel Density For Quantity Deviations (Indonesia)
density: devqty_without density: devqty_with
.969433
0
-1 0 1
quantity_deviation
Indonesia
40
Figure 8: First Order Stochastic Dominance
F1
F2
x
f2 f1
x
Figure 9: CDFs for Argentina (values)
CDF Argentina
1.2
1
0.8
without PSI
0.6
with PSI
0.4
0.2
0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
41
Figure 10: CDFs for the Philippines (values)
CDF Philippines
1.2
1
0.8
without PSI
0.6
with PSI
0.4
0.2
0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Figure 11: CDFs for Indonesia (values)
CDF Indonesia
1.2
1
0.8
with PSI
0.6
without PSI
0.4
0.2
0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
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