metadata: authors: 0: author: Hillberry,Russell Henry
1: author: Karabay,Bilgehan
2: author: Tan,Shawn Weiming
count: World
docna: 0: docna: Risk Management in Border Inspection
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Human Rights,Trade Facilitation,Health Care Services Industry,Trade and Services
teratopic: Law and Development,Industry,International Economics and Trade
abstracts: cdata!: As part of their commitments under the
            World Trade Organization's Agreement on Trade
            Facilitation, many developing countries are set to adopt
            risk management, a strategy for selecting import shipments
            for inspection. This paper formalizes key enforcement issues
            related to risk management. It argues that the complexities
            of international trade oversight mean that inspecting
            agencies lack certainty about the conditional probability
            that a given shipment will not comply with import
            regulations. Ambiguity of this sort is likely to be
            important in developing countries that lack the
            sophisticated information technology (IT) used in advanced
            risk management systems. This paper show empirically that
            infrequent shipments have conditionally higher inspection
            rates, a finding that is consistent with the ambiguity
            hypothesis. This paper formalizes a role for ambiguity in a
            theoretical model of border inspection. Finally, the paper
            calibrates the model and shock the ambiguity parameters to
            illustrate the consequences of an IT -driven improvement in
            risk management capabilities for search and compliance.
repnme: repnme: Risk Management in Border Inspection
display_title: Risk Management in Border Inspection
listing_relative_url: /research/2020/10/32485379/risk-management-border-inspection
topicv3: Trade m1326924 698,Trade in Services m1326928 780,Trade Facilitation and Logistics m1327174 772,Health m1504661 3480,Discrimination m1505707 3379
publishtoextweb_dt: 2020-10-14T00:00:00Z
historic_topic: Law and Development,Industry,International Economics and Trade
origu: EFI-EAP-FCI-Finance-1 (EEAF1)
no_of_pages: 46
author_keys: 0: author_key: 1228415
1: author_key: 1300209
2: author_key: 1239884
model_extractions: Policy Research Working Paper 9438 Risk Management in Border Inspection _Russell Hillberry Bilgehan Karabay Shawn W. Tan_ Finance, Competitiveness and Innovation Global Practice October 2020
Policy Research Working Paper 9438

# **Abstract**

As part of their commitments under the World Trade Organization’s Agreement on Trade Facilitation, many developing countries are set to adopt risk management, a strategy for selecting import shipments for inspection. This paper formalizes key enforcement issues related to risk management. It argues that the complexities of international trade oversight mean that inspecting agencies lack certainty about the conditional probability that a given shipment will not comply with import regulations. Ambiguity of this sort is likely to be important in developing countries that lack the sophisticated information technology (IT) used in advanced risk management systems. This paper show empirically that infrequent shipments have conditionally higher inspection rates, a finding that is consistent with the ambiguity hypothesis. This paper formalizes a role for ambiguity in a theoretical model of border inspection. Finally, the paper calibrates the model and shock the ambiguity parameters to illustrate the consequences of an IT -driven improvement in risk management capabilities for search and compliance.

This paper is a product of the Finance, Competitiveness and Innovation Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at swtan@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Risk Management in Border Inspection<sup>∗</sup>

Russell Hillberry<sup>†</sup> Bilgehan Karabay<sup>‡</sup> Shawn W. Tan<sup>§</sup>

## **Abstract**

As part of their commitments under the WTO’s Agreement on Trade Facilitation, many developing countries will adopt risk management, a strategy for selecting import shipments for inspection. In this paper we formalize key enforcement issues related to risk management. We argue that the complexities of international trade oversight mean that inspecting agencies lack certainty about the conditional probability that a given shipment will comply with import regulations. Ambiguity of this sort is likely to be important in developing countries that lack the sophisticated information techOriginally published in the nology (IT) used in advanced <u>Policy Research Working Paper Series</u> risk management. We show empirically <u>on</u> _October 2020._ that infrequent This version is updated on shipments have _June 2021._ conditionally <u>higher inspection rates, a fnding</u> that is consistent with To obtain the originally published version, please email our ambiguity hypothesis. We formalize a role for ambi <u>prwp@worldbank.org guity</u> in a theoretical <u>.</u> model of border inspection. We calibrate the model and shock the ambiguity parameters to illustrate the consequences of an IT-driven improvement in risk management capabilities for search and compliance.

Keywords: Trade Facilitation; Risk Management; Border Inspection; Ambiguity; Choquet Expected Utility.

JEL classification: D73; D81; F18.

> ∗We would like to thank Evgenii Monastyrenko, the participants at the 13th Australasian Trade Workshop (ATW), members of the Purdue University trade brownbag, and two anonymous referees for comments on earlier drafts. Research for this paper has been supported in part by the governments of Norway, Sweden, and the United Kingdom through the Multidonor Trust Fund for Trade and Development, and by the UK Department for International Development (DFID) through the Strategic Research Partnership on Economic Development. This work was also supported by the USDA National Institute of Food and Agriculture, Hatch project 1013622. The views expressed herein are those of the authors and should not be attributed to the World Bank, their Executive Boards, or management. All errors are our own.

> †Department of Agricultural Economics, Purdue University, Krannert Bld., Room 564, 403 W. State Street, West Lafayette, IN 47907, USA. Tel: +1 (765) 494 4249. E-mail: rhillber@purdue.edu. URL: http://www.russellhillberry.net.

> ‡School of Economics, Finance and Marketing, RMIT University, 445 Swanston Street, Bld. 80, Level 11, Melbourne, VIC 3000, Australia. Tel: +61 (3) 9925 5867. E-mail: bilgehan.karabay@gmail.com. URL: http://bilgehan.karabay.googlepages.com.

> §The World Bank. 1818 H Street, N.W. Washington, DC 20433 USA. Tel: +1 (202) 473 7621. E-mail: swtan@worldbank.org.
# **1 Introduction**

Effective oversight of imported goods shipments contributes to a wide variety of public policy goals, including revenue collection, law enforcement, and the protection of human, animal and plant health. In many of these policy areas a single non-compliant import shipment can cause enormous damage, economic or otherwise. National governments often attempt to control such risks by authorizing frequent inspections of imported goods, even in situations where the vast majority of shipments satisfy import regulations. But frequent and burdensome inspections also act as frictions that inhibit international trade.

The World Trade Organization’s _Agreement on Trade Facilitation_ (TFA) contains a broad body of reform measures that are meant to expedite the movement of international goods trade. A key reform in this package is risk management, a strategy for selecting imported goods shipments for inspection. Effective risk management focuses inspection resources on shipments that are at high-risk for non-compliance with import regulations while reducing the inspection burden on low-risk shipments. Reforms of this kind typically include the adoption of sophisticated information technology (IT) that is used to communicate information about the shipment, assess risk, and store inspection results for the purposes of ongoing improvements in risk assessment. Implementation of modern risk management methods requires inspecting agencies to make multi-year investments in IT, and in retraining their staff. A better understanding of the nature and size of the benefits from reform can inform the decision of when and where to implement it.

In this paper we identify and study a key challenge for border inspection agencies: uncertainty surrounding their conditional forecast of the probability that a particular import shipment complies with import regulations. _Ambiguity_ of this kind is important in the international trade context because agencies tasked with oversight of import shipments must consider a wide range of potential harms related to thousands of different products sourced from dozens of countries and involving countless trading firms.<sup>1</sup> This problem is compounded

> 1The harms that we consider are broad, including tariff evasion, violation of food safety or other product standards, invasive species and other environmental harms such as plant and animal health. Harm associated with smuggled contraband can be mapped onto our model, but perhaps not as cleanly as other types of non-

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by the fact that many types of shipments are only rarely observed, which can mean that developing country inspection agencies that lack appropriate IT may not be able to recall the outcome of a previous inspection, or even to know whether or not an unusual shipment type has been observed/inspected in the past.<sup>2</sup> We argue that a key contribution of modern IT in this setting is to reduce ambiguity; the information storage and analytical tools that modern systems provide allow the inspecting agency to better use information from the import declaration to predict the conditional probability that a given shipment is non-compliant. Improved capacity to predict non-compliance leads to a better allocation of inspection resources, allowing key enforcement goals to be reached, even as the overall inspection burden is reduced. These are the primary goals of most risk management reforms.

Our focus on ambiguity is motivated by discussions with operational experts in trade logistics, but we also motivate this focus with stylized facts about conditional inspection rates in data from the Serbian customs agency. The data do not allow us to measure ambiguity directly, but we are able to show that shipment types that were more frequently observed in the prior year are less likely to be inspected in the current year. The negative relationship between lagged shipment frequency and the inspection rate remains, even after we control for heterogeneous risks. Although greater ambiguity about the compliance of infrequent shipments is not the only explanation for this empirical result, we maintain that - in the context of international trade - ambiguity is likely to be a quantitatively important explanation for the fact pattern we observe. While our theory is applicable to both developed and developing countries, the quantitative importance of ambiguity is likely to be much larger in developing country inspection agencies that lack sophisticated IT.

We develop a theoretical model that links the equilibrium allocation of inspection resources to the underlying probabilities of non-compliance and to ambiguity surrounding those compliance with import regulations.

> 2During field work in a middle-income country, one of the authors visited a border station in which an agency tasked with inspecting imports for sanitary risks stored its inspection records in paper form. The documents from several prior years were kept in large canvas bags piled together in the corner of a room. It is unlikely that these records were at all useful for informing subsequent inspection decisions in real time. The information that was retained may well have resided only in the minds of individual inspectors.

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probabilities. Our framework for incorporating ambiguity in the inspection decision is a form of Choquet Expected Utility (CEU) theory, as described in Schmeidler (1989). In CEU theory, inspectors’ beliefs about probabilities of non-compliance are represented as normalized and monotone set functions known as _capacities_ . Importantly, capacities allow the model to separate inspectors’ beliefs from the conditional probability that a good is non-compliant (in contrast to standard assumptions about beliefs in the expected utility framework). We adopt a particular form of capacities: the non-extreme-outcome additive (neo-additive) capacity described in Chateauneuf _et al._ (2007). In addition to a parameter that defines the ambiguity surrounding each type of shipment, the framework describes (in terms labeled _optimism_ or _pessimism_ ) how the agency’s beliefs about levels of compliance among unsearched shipments differ from the underlying probabilities. We show that a resource-constrained agency that is sufficiently pessimistic will inspect shipments with greater levels of ambiguity more frequently. While this is optimal behavior given the agency’s objective function, relative to a no-ambiguity benchmark the agency’s search activity is misallocated.

We develop this framework to illustrate the manner in which ambiguity-reducing investments in IT can contribute to successful risk management reforms. The goals of modern risk management reforms are typically to reduce the overall inspection burden while improving (or at least maintaining) compliance. We calibrate a numeric version of the model to the Serbian customs data (which represent a post-reform equilibrium) and consider the effects of substantially increased ambiguity on equilibrium rates of inspection and compliance (a reverse reform). The agency responds to higher levels of ambiguity by shifting even more inspection resources towards the shipments about which there is greater ambiguity (i.e., the infrequent shipments) and this reduces the effectiveness of search as a deterrent against non-compliance among other types of shipments. In order to maintain compliance in the face of increased ambiguity the agency must undertake increased levels of search. Modern reforms reverse this dynamic; IT investments that reduce ambiguity allow better targeting of search activity, which maintains or improves compliance, even as levels of search activity are dramatically reduced. Our calibrated model produces changes in inspection activity that 3
are comparable to those of reforms observed in real world settings.

Our paper is closely related to an existing literature that studies police searches of civilians for contraband, and in that context formalizes conditions that would constitute racial or other kinds of discrimination in police search behavior. Knowles _et al._ (2001) and Persico (2002) use an expected utility framework to formalize the decision to search an individual and/or his property (e.g., automobile).<sup>3</sup> An implication of expected utility theory is that – the police officer is assumed to know, with certainty, the probability conditional on an – observable characteristic or characteristics such as the civilian’s race that a search of an individual or her automobile will find contraband. Our primary departure from this literature is formalizing a role for ambiguity about the underlying probability distribution. It is likely that ambiguity is more important in the international trade context given (a) the large number of characteristics of an import shipment, and (b) the fact that many import shipments have bundles of characteristics that are only rarely observed together.<sup>4</sup> We also – focus on overall search intensities and compliance rather than discrimination with respect – to characteristics since the equal protection issues important for police searches are less relevant in the context we study.<sup>5</sup> In the border management context, risk management generates very different search intensities for shipments with different characteristics (e.g., product type and/or country of origin), an outcome that the police search literature would likely attribute to bias. In this respect, our paper is also related to a small but growing literature on inaccurate statistical discrimination. Bohren _et al._ (2020) show that statistical discrimination that is based on inaccurate beliefs about decision-relevant characteristics can

> 3A user-friendly introduction to those papers can be found in Persico and Todd (2008), which also discusses some caveats to the theory. Another related paper is Eeckhout _et al._ (2010), which shows that random crackdowns can be an optimal policing strategy. Lazear (2006)’s paper on high-stakes testing in education is also relevant for its potential applicability to crime.

> 4Armenter and Koren (2014) show that, even in U.S. data, trade data are extremely sparse. The most common number of shipments for a product-country-firm observation is one. Related facts have been observed in data from other countries. Our data from Serbia offer an example.

> 5Furthermore, while we focus on the planner’s problem (i.e., the inspecting agency), both Knowles _et al._ (2001) and Persico (2002) look at the optimal behavior of a single officer (among many) to determine if there is any discrimination in equilibrium. This distinction is important since when deciding on search intensity, the agency takes into account the effect of its decision on the overall compliance rate, whereas the individual does not.

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also be attributed to bias or prejudice.<sup>6</sup> Our paper is also related to papers that study probabilistic approaches to enforcement in other settings. Teitelbaum (2007) examines a unilateral accident model with ambiguity and constructs an efficient ambiguity-adjusted liability rule in a legal setting. In an audit context, Bigus (2012) models unilateral auditor liability under ambiguity aversion. Another application area is the prevention of tax evasion. The theory of tax evasion began with the seminal work of Allingham and Sandmo (1972) and has been primarily grounded in the expected utility framework (for a review of this literature, see Sandmo, 2005).<sup>7</sup> A paper with similar implications to ours (though it employs a different theoretical mechanism) is Kuchumova (2017), who shows how the use of third party information about taxpayers’ incomes can reduce the tax agency’s reliance on audits.<sup>8</sup> The operational literature on risk management in border inspection is typically less formal than what we offer here. Widdowson and Holloway (2011) describe risk management using a heuristic framework that can be understood in terms of expected utility theory.<sup>9</sup> Our conversations about best practices with World Bank operational experts in developing country border management suggest an important role for ambiguity. For example, one practice described in these discussions is to conduct a full physical inspection for each new combination of product, origin country, and firms involved in import transactions.<sup>10</sup> This strategy represents an effort to respond to ambiguity.

A small empirical literature has studied the operation of risk management and/or the

> 6In the economics literature, most studies consider two sources of discrimination: taste-based and beliefbased (statistical). While taste-based discrimination is an indication of decision-makers’ prejudice, beliefbased discrimination refers to differential treatment of individuals due to decision-makers’ beliefs on their decision-relevant characteristics. Bohren _et al._ (2020) show that when these beliefs are inaccurate, there is an identification problem in determining the source of discrimination. One role of ambiguity in our setting is that it generates inaccurate beliefs about the underlying probabilities of compliance.

> 7There are some notable exceptions. To explain tax compliance behavior, Bernasconi (1998) uses rankdependent expected utility, whereas Snow and Warren (2005) employ ambiguity preferences that represent taxpayers’ attitudes towards the uncertainty of audit probability.

> 8Kuchumova writes, for example, that in her model “the tax authority should focus audits on those taxpayers about whom it has less accurate signals” (p.163).

> 9For example, Table 6.1 on p.104 in Widdowson and Holloway (2011) presents a risk matrix with ‘likelihood’ along one axis and ‘consequence’ along the other.

> 10We thank Lazar Ristic of the World Bank for providing us with this example.

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effects of reform episodes related to the oversight of international goods trade. Martincus _et al._ (2015) show that inspections impede exporting in a study of the risk management system that governs Uruguayan exports. Fernandes _et al._ (2021) conduct an evaluation of the effects of reduced inspections of import shipments by Albanian customs during a period of substantial reform. Fernandes _et al._ (2017) evaluate preliminary steps towards a reform undertaken by the Food and Veterinary Agency of North Macedonia. Cariolle _et al._ (2019) and Chalendard _et al._ (2019) show how external information on trade flows can be used to forecast tariff evasion in Gabon and Madagascar, respectively.

In this paper we isolate a channel through which risk management reforms contribute to better border management. We argue that the rarity of many types of import shipments makes untenable a presumption that inspecting agencies are fully informed about the conditional probability that a shipment does not comply with import regulations. It is likely that modern IT systems substantially reduce ambiguity by improving the agency’s conditional forecast of the probability that a shipment complies with import regulations. To motivate our focus on ambiguity, we introduce a new stylized fact - shipments that were less frequently observed in prior years are conditionally more likely to be inspected. We apply tools from decision theory to understand inspecting agencies’ likely response to ambiguity, and the manner in which ambiguity-reducing investments in IT are likely to shift inspection resources. Finally, we calibrate the model to illustrate quantitative relationships between ambiguity, search intensities and firms’ compliance with import regulations.

The rest of the paper is organized as follows. Section 2 briefly describes the operation of modern risk management systems as they apply to oversight of imported goods shipments. Section 3 motivates our focus on ambiguity with stylized facts from the Serbian customs data. Section 4 develops the theoretical framework incorporating ambiguity, describes the equilibrium, and derives comparative static predictions of the model. Section 5 calibrates a numerical version of the model and conducts counterfactual analysis. Section 6 concludes. The general framework describing the neo-additive capacity and the Choquet integral is relegated to the appendix as are additional details about the model calibration and conventional 6
summary statistics of variables in the data.

# **2 Risk-based methods in border management**

Risk-based approaches to inspection have become a central component of border management in developed countries. Risk management is considered to be a ‘best practice’ strategy in the oversight of international goods trade. It appears in international agreements such as the World Customs Organization’s _Revised Kyoto Convention_ and the TFA. In most developing countries the customs agency already employs some form of risk management, though improvements are often necessary. A more difficult step is the adoption of risk-based inspection methods in so-called ‘technical’ agencies, those responsible for ensuring compliance with regulations concerning food safety, human and animal health, and the environment.<sup>11</sup> In this section we sketch the outlines of a reform episode that implements modern risk management strategies that include advanced IT. Prior to a reform, analysis of available data on inspections often finds very high rates of inspection, paired with relatively low rates of failed inspections.<sup>12</sup> These outcomes suggest that better targeting of inspections toward risky shipments would identify a larger proportion of the non-compliant shipments, even while the overall inspection burden were reduced.<sup>13</sup> The absence of coordinated risk assessment may mean that one source of poor targeting is heterogeneous priors – across individual inspectors or across inspection teams located at different control points – about conditional probabilities of non-compliance. Risk management reforms typically centralize the task of risk assessment, improve the quality of data available for making those assessments, and improve the system’s

> 11Technical agencies oversee the movement of fewer shipments than the customs agency, but also conduct more intrusive inspections – including lab tests, for example. They are also usually less well-resourced than the customs agency and subsequently less likely to have adopted modern risk management methods involving IT. Fernandes _et al._ (2017) study a partial reform in a technical agency.

> 12 See descriptions of pre-reform environments in Konar-Leacy _et al._ (2019) and in Fernandes _et al_ . (2021).

> 13An aspect of the problem that is not addressed in our theory - but one that is also likely to be relevant to the issues discussed here - is that the high volume of inspections undertaken prior to reform may lead inspections to be insufficiently thorough. Low rates of failed inspections in the pre-reform period can be explained by poor targeting alone, but lax inspections may also contribute to this outcome. In this paper, we do not model changes in the thoroughness of inspections, but further optimization over the thoroughness of inspections represents an additional benefit of improved targeting. We thank an anonymous referee for pointing out this additional margin of adjustment to reform.

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capacity to forecast probabilities of non-compliance.

In the initial stages of a reform, a committee of centrally-located experts (often aided by foreign expertise) define the range of potential harms that inspections are meant to avoid and associate likely harms with non-compliant imports of particular products. The central committee also gathers available information from past inspections to understand the frequency and types of non-compliance, and the distribution of non-compliance across a wide range of shipment characteristics. The information on harms and on non-compliant imports is combined to inform a national strategy that generates different _a priori_ inspection probabilities across shipments based on the outcome of a rigorous risk assessment process.

Another central component of reform is the adoption of advanced IT systems.<sup>14</sup> These systems facilitate risk management in a number of ways. First, they allow reliable electronic storage and fast recall of detailed information on past inspection activity and outcomes. Second, IT systems combine detailed information from the import declaration on the shipment’s characteristics with the parameters set by the central committee to make a rapid determination of the risk posed by each shipment. Third, IT can improve compliance forecasts for the less-frequently-observed shipments with statistical analysis of more frequent shipments that share important characteristics with the infrequent shipments. Finally, by facilitating – rapid communication including guidance from the center on news of emerging hazards, or communication to the center of changes in non-compliance rates on the ground – IT helps inspecting agencies to rapidly update the conditional priors that guide the inspection decision in times when compliance rates are changing.

Once it is operational, the risk management system operates as follows. Information from the central committee parameterizes a risk model using information on the severity of harm from non-compliant imports of a given product and past evidence of the likelihood of non-compliance of shipments with different characteristics. When imported goods arrive at a port, border crossing or other inspection location, the trading firm files an import 14A common IT system used in developing country customs agencies is ASYCUDA, a low-cost, off-theshelf risk management system developed by the United Nations Committee for Trade and Development. Even when the purchase price of IT systems is low, agencies must spend considerable resources on retraining personnel to use such systems effectively.

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declaration. The import declaration provides details about one or more import transactions, – and for each transaction provides information for a large number of data fields including country of origin, a detailed product classification, and a complete listing of firms involved in the transaction and in the logistics supply chain.<sup>15</sup> The risk management system applies predetermined weights to data in each of these fields, as well as information on the scale of possible harms associated with a non-compliant shipment of this type, to generate a ‘risk score’ that is used to determine whether or not the goods will be inspected. Inspectors conduct the search when the system recommends it.<sup>16</sup> The outcome of the search is recorded electronically, and communicated to the central committee for the purposes of updating the risk model.

# **2.1 Effects of information technology on system performance**

In our view the four contributions of IT listed above can be understood as effectively reducing the ambiguity surrounding the inspecting agency’s _ex ante_ expectation of the probability that a shipment with given observable characteristics will not be compliant with import regulations. Improved capabilities of storage and recall allow the history of a shipment with given characteristics to better inform the agency’s forecast of non-compliance for shipments with the same bundle of characteristics. Information from frequently observed shipments can be used to estimate the marginal contribution of specific shipment characteristics to compliance, thereby improving the agency’s forecast of compliance probabilities for less frequently-observed shipments with similar characteristics. The combination of nationally-collected information on relationships between shipment characteristics and non-compliance, together with a common well-defined understanding of possible harms, reduces heterogeneity in the inspection decision that might otherwise exist across individual inspectors or inspecting offices. The IT system’s ability to facilitate the rapid flow of ac-

> 15Most declarations document details for a single transaction, but some declarations contain many. We use transactions as our unit of analysis since transactions map to a single combination of product, origin country and firm.

> 16Inspectors usually have the capacity to deepen the search based on their initial findings. In some contexts they may also have autonomy to initiate a search without guidance from the system, though this would be rare when compared to searches initiated because of guidance from the IT system.

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curate information allows expeditious updating of _ex ante_ probabilities as new information emerges. All these features of IT act to compress realized variation in the conditional forecast of the probability of non-compliance. This motivates our analysis of reduced ambiguity in the theoretical model.

# **3 Descriptive evidence**

In this section, we use data provided by the Serbian customs agency to support two arguments that are central to the paper: (1) ambiguity is a pervasive phenomenon in the oversight of import shipments, and (2) agencies with oversight responsibilities respond to ambiguity when allocating scarce inspection resources. We lack a direct measure of ambiguity, so our arguments are necessarily indirect. In our view, a primary source of ambiguity in the oversight of import shipments is the infrequency with which inspecting agencies observe many shipment types. We use the frequency with which shipment types are observed as an inverse proxy for ambiguity. We show that shipment types that are infrequently observed are numerous and that infrequently observed shipment types are inspected at higher rates. The negative relationship between inspection rates and shipment frequency remains, even after controlling for available indicators of risk.

The Serbian customs agency already operates under risk management protocols that exploit sophisticated IT. Since our thesis is that risk management involving IT reduces the salience of ambiguity in the inspection decision, the agency’s response to ambiguity is likely to be muted relative to what one would observe in a pre-reform environment. For our purposes, it would be preferable to use data from a pre-reform environment, but unfortunately agencies that have not adopted modern IT usually lack the high quality data necessary for our exercise. We use the Serbian customs data because it is high quality and because it is available to us.

The Serbian customs agency provided us with comprehensive data for the years 2006-16. The raw data are defined at the level of an import transaction (hereafter, a shipment). Each shipment record contains information about the shipment’s value, weight, origin country, associated duties and taxes paid, the importing firm’s identity, 10-digit Harmonized System 10
(HS) product code and the type of inspection that was conducted, if any. Importing firms are identified by their unique tax identification number. We further restrict the data to imports of products that will be consumed in Serbia and exclude imports that are temporary, for inward processing or for re-export. We report results from a 2013-16 sub-sample of the data that maintains a consistent classification of HS10 products.<sup>17</sup> We define the shipment _type_ at the level of the origin country ( _o_ ), importing firm ( _f_ ), and HS10 product ( _k_ ).<sup>18</sup> We aggregate these data to the _ofkt_ level, where _t_ represents a calendar year. Our primary interest is in the relationship between current-year inspection rates in an _ofk_ triplet and the numbers of shipments in the same triplet that were observed by the agency in the previous year. To study this relationship flexibly, we create bins of different lagged shipment frequencies and estimate the effects of dummy variables attached to each frequency bin. Our frequency bins have observations with 0, 1, 2, 3-5, 6-10, 11-100, and 100+ lagged shipments, respectively.<sup>19</sup> A key outcome for each shipment is whether or not it is inspected. In Serbia, each shipment is subject to six classes of documentary and/or physical inspections.<sup>20</sup> We collapse this detail, determining only whether a shipment underwent any kind of inspection, or was not inspected.<sup>21</sup> The primary outcome variable we study is the inspection rate, which is

> 17We observe similar results at the HS6 level for this sub-sample and for HS6 estimates over the entire sample. An earlier version of this paper, Hillberry _et al._ (2020), reports results using the entire data set at the HS6 level. Those specifications did not include the additional risk variables that we include here.

> 18The only firm about which we have information in our data is the importing firm _f_ . The agency’s risk model would also incorporate into its analysis the identity of other firms in the supply chain, including the (foreign) exporting firm and the firms involved in transportation of the goods. While not ideal, the absence of data on the other firms involved in the transaction may not be as problematic as it might seem, since importing firms often maintain stable supply chains. Carballo _et al._ (2014) provide some evidence on this point, showing that Peruvian importers have a median of only 1 exporter per HS10 product-origin country pair, and an average of only 1 _._ 279 exporters.

19Our chosen binning strategy provides considerable flexibility at the low end of the frequency distribution. We also tried an alternative binning strategy that shifted flexibility towards the middle of the distribution and found similar (unreported) results.

> 20We exclude from the data shipments that are never inspected due to their product characteristics: trade in natural gas or electricity transported through pipelines and electrical power lines. These shipments are distinct from shipments that are not subjected to physical inspections through a determination of the customs agency (type 1).

> 21One class of inspections in the data are _documentary_ inspections that include no physical inspection. On the grounds that purely documentary inspections may be relatively unobtrusive, we experimented with treating shipments subject only to documentary inspections as ‘not inspected.’ Purely documentary ship-

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Table 1: Lagged shipment frequencies and shares of 2016 import statistics

|# of shipments|Share of|Share of|Share of|Share of|
|---|---|---|---|---|
|observed in 2015|shipment types|transactions|inspections|import value|
|0|0.539|0.188|0.350|0.191|
|1|0.131|0.051|0.047|0.039|
|2|0.075|0.038|0.033|0.032|
|3-5|0.108|0.084|0.068|0.071|
|6-10|0.064|0.089|0.068|0.086|
|11-100|0.079|0.374|0.291|0.392|
|_>_100|0.005|0.176|0.143|0.189|
|Totals:|671,548|3,889,775|285,611|1,597,102|

Table notes: The table shows, for frequency bins defined over 2015 imports, the share of shipment types ( _ofk_ triplets), import transactions, inspections and import value in Serbia’s 2016 imports. The final row reports the total associated with each variable. Import value is reported in millions of Serbian dinars.

calculated as the ratio of inspected shipments to shipments in year _t_ , for an _ofk_ triplet, multiplied by 100.

We begin by showing the distribution of import and inspection activity across the lagged shipment frequency bins. Table 1 reports, for 2016 Serbian imports at the HS10 level, a collection of summary statistics for each lagged shipment frequency bin. We report each bin’s share of shipment types ( _ofk_ observations), total transactions, total inspections and import value. The final row of the table reports totals for each outcome variable.<sup>22</sup> The first column shows that infrequently observed shipment types are a large majority of all shipment types observed. 54 percent of _ofk_ triplets were not observed in the prior year. Another 31 percent of shipment types were observed five or fewer times during the previous year. The sheer volume of infrequently observed shipment types poses a fundamental challenge for border inspection agencies. They have very little prior information to inform their compliance forecasts for a large majority of the _ofk_ triplets they must oversee.

> ments represent a relatively small share (of inspections, and of shipments) in our data, so the treatment of these shipments had no material effect on the results. The results we report use the broadest definition of inspections, treating documentary inspections as inspections.

> 22In appendix A we report a table of conventional summary statistics for the variables used in our subsequent regression analysis. That table contains much of the information reported here, but the data are not as useful for expositional purposes.

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The second column reports each bin’s share of the total number of import transactions. Shipment types that were observed more frequently in the previous year account for a much larger share of transactions; a sizable share of import activity is undertaken by firms that routinely import the same items from the same countries. The relatively larger sample sizes should allow the agency to make a more accurate forecast of compliance probabilities for these shipments. Infrequently observed shipment types still constitute a significant share of total import transactions. Shipment types that had not been observed at all in the previous year account for 19 percent of import transactions. Shipment types that were observed between one and five times in the previous year account for another 17 percent. In other words, more than one third of all import transactions relate to shipment types that had been observed five times or fewer in the previous year. Managing such a large volume of rarely seen shipments is a difficult problem, and would be even more difficult without adequate IT.

So how does the Serbian customs agency treat infrequently observed shipment types? It inspects them at much higher rates than others. In 2016, _ofk_ triplets that had not been observed in the prior year made up 19 percent of transactions, but accounted for 35 percent of all inspections. Meanwhile, shipments that were observed more than 10 times in the prior year accounted for 55 percent of transactions but only 43 percent of inspections. Our hypothesis is that one reason infrequently observed shipment types are more likely to be inspected is that infrequency generates ambiguity about the conditional forecast of the probability the shipment is compliant. The inspecting agency responds to this ambiguity with greater search.

All of the statistics in Table 1 are unconditional; they do not take into account heterogeneity across shipment types in compliance probabilities or in the expected harm associated with a non-compliant shipment. Since the Serbian customs agency already employs modern risk management tools, the distribution of inspection activity also depends on those factors. If we had sufficient data to forecast accurately the compliance probabilities (and if we had estimates of the expected harms from non-compliance), we could use that forecast to 13
determine whether the agency is ‘oversampling’ infrequent shipments.<sup>23</sup> While we lack the precise data that would allow us to make conditional forecasts of non-compliance, we have several variables that are likely to be good proxies for import customs risk. First, we calculate the prior year’s inspection rate for each observation for which there were shipments in the prior year.<sup>24</sup> Shipment characteristics associated with expected non-compliance and/or expected harm are likely to be strongly correlated over time, so lagged inspection rates are likely to be a good proxy for risk in the current period. Second, we include the product’s unit value. Deviations of unit values from their expected value may generate inspections. Third, we include the _ad valorem_ tariff collected at the border. Finally, we include a measure of the tendency for an _ofk_ triplet to be included on import declarations with other transactions. We count the average number of products per declaration on declarations that contain each _ofk_ triplet, and include this as an independent variable in the regression. Declarations that contain more products are more likely to be inspected.<sup>25</sup> In order to avoid aggregation issues, we estimate at the finest level of aggregation, HS10.<sup>26</sup> We include product- and origin country-fixed effects in our specifications because these characteristics of an _ofk_ triplet are the two about which the risk assessment process is likely to generate the best informed priors. In some specifications we also include fixed effects that sweep out variation in inspection rates across importing firms. It is likely that firm fixed effects sweep out ambiguity as well as predictable risks.<sup>27</sup>

> 23One piece of data that the agency has, and we do not, are the outcomes of previous inspections. These are a critical input into risk management, as they are likely to be highly informative about future compliance probabilities. Such data are highly confidential, and not available to us.

> 24Shipments that were not observed in the prior year are coded with a lagged inspection rate of zero.

> 25A higher inspection rate for goods in declarations with more product types may be the result of the inspection decision depending on the riskiest element on the import declaration.

> 26In a previous version of the paper, we did our estimations at the level of an HS6 category since these categories were more stable over time. Within-product variation in risks may lead such estimates to be biased. We thank two anonymous referees for suggesting estimation at the finer level.

> 27Consider this simply as a sample size issue. The agency will have relatively large samples of observations at the level of countries and products. But many importing firms would have been observed rarely, if at all. The agency is unlikely to have enough information to make accurate and unbiased compliance forecasts for such firms. Firm fixed effects sweep out variation between frequent and infrequent importers, which is precisely the kind of variation that we wish to exploit.

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The relationship that most interests us is the relationship between lagged shipment frequency and the current-year inspection rate. To capture this we include dummy variables for each lagged shipment frequency bin. The excluded category is the bin with shipment types that were not observed in the prior year. We also include a continuous measure of lagged shipment frequency. This captures the average _within-bin_ relationship between lagged shipment frequency and inspections.

We estimate via OLS, using the estimation specification that follows: where _IRt_<sup>_ofk_</sup> is the inspection rate for a given _ofk_ triplet in year _t_ , **Θ** is a vector of regression coefficients, each associated with one of the dummy variables in **Bin**<sup>**ofk**</sup> **t** _−_ **1**<sup>,avectorof</sup> lagged shipment frequency dummies, _Ship_<sup>_ofk_</sup> _t−_ 1<sup>isacontinuousmeasureoflaggedshipment</sup> frequency, and _β_ is its associated coefficient, **Risk**<sup>**ofk**</sup> is a vector of variables meant to capture underlying variation in compliance probabilities and expected harms, **Ω** is a vector of coefficients associated with the risk variables, _γt_<sup>_ok_</sup> is a product-origin country fixed effect, _δt_<sup>_f_</sup> is a firm fixed effect, and _ε_<sup>_ofk_</sup> _t_ is a normally distributed error term. Because our theoretical model attempts to explain the allocation of inspection resources across shipments within a given period of time, our preferred specifications are single year cross-sections in which the _t_ subscript is irrelevant.

Table 2 reports cross-sectional results for 2016, and from a pooled regression over the years 2013-16.<sup>28</sup> The first column of results shows inspection activity across shipment size bins, using fixed effects to control for variation at the origin country - HS10 product level. With the bin containing shipments that were not observed in the previous year as the excluded category, we find that all the coefficients on the remaining bin dummies are negative and statistically significant. Shipment types that were observed just one time in the prior year were inspected 2 _._ 2 fewer times per 100 shipments than those that were not observed. Shipment types that were observed more than 100 times in 2015 were inspected 4 _._ 5 fewer times per 100 shipments than were previously unobserved types. These cross-bin differences

> 28Unpublished cross-sectional results for 2013 look quite similar.

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Table 2: Inspection rates and lagged shipment frequency

||2016|2016|2016|2016|2013-16|2013-16|
|---|---|---|---|---|---|---|
|Bin_n_=1|-2.195***<br>(0.089)|-2.192***<br>(0.089)|-3.645***<br>(0.123)|-0.335***<br>(0.070)|-3.659***<br>(0.113)|-0.241***<br>(0.038)|
|Bin_n_=2|-2.466***|-2.459***|-3.936***|-0.339***|-3.953***|-0.222***|
||(0.107)|(0.107)|(0.139)|(0.077)|(0.121)|(0.042)|
|Bin_n∈_[3_−_5]|-3.060***|-3.047***|-4.521***|-0.316***|-4.399***|-0.208***|
||(0.108)|(0.108)|(0.146)|(0.068)|(0.128)|(0.036)|
|Bin_n∈_[6_−_10]|-3.381***<br>(0.122)|-3.356***<br>(0.121)|-4.928***<br>(0.162)|-0.405***<br>(0.070)|-4.871***<br>(0.149)|-0.268***<br>(0.037)|
|Bin_n∈_[11_−_100]|-3.468***|-3.377***|-5.320***|-0.255***|-5.256***|-0.205***|
||(0.125)|(0.125)|(0.177)|(0.066)|(0.170)|(0.035)|
|Bin_n>_100|-4.543***<br>(0.228)|-3.859***<br>(0.265)|-6.212***<br>(0.380)|-0.259*<br>(0.144)|-5.787***<br>(0.326)|-0.266***<br>(0.082)|
|Ship_t−_1||-0.003***<br>(0.001)|-0.006***<br>(0.002)|-0.001<br>(0.001)|-0.006***<br>(0.001)|-0.000<br>(0.000)|
|Insp_t−_1|||0.196***<br>(0.010)|0.050***<br>(0.003)|0.180***<br>(0.009)|0.032***<br>(0.002)|
|ln UV_t_|||-1.484***|-0.085***|-1.490***|-0.052***|
||||(0.064)|(0.018)|(0.061)|(0.010)|
|AV tarif_t_|||0.022|0.010|0.001|-0.000|
||||(0.015)|(0.008)|(0.003)|(0.001)|
|Multi-goods|||0.082***|0.010***|0.082***|0.005***|
||||(0.004)|(0.003)|(0.004)|(0.001)|
|Product x Origin|Yes|Yes|Yes|Yes|No|No|
|Product x Origin x Year|No|No|No|No|Yes|Yes|
|Firm|No|No|No|Yes|No|No|
|Firm x Year|No|No|No|No|No|Yes|
|R<sup>2</sup>|0.430|0.430|0.448|0.667|0.455|0.680|
|Adjusted-within-R<sup>2</sup>|0.005|0.005|0.036|0.001|0.034|0.001|
|N|627927|627927|627903|621830|2263449|2239590|

Table notes: Regressions for 2016, and for pooled regressions over the entire 2013-16 period. Data are annual totals or rates calculated for triplets defined by shipments associated with a given combination of HS10 product, origin country and importing firm. The dependent variable is the inspection rate. The independent variables of interest are dummy variables indicating lagged shipment frequency bins and the continuous lagged shipment frequency measure, _Ship_<sup>_ofk_</sup> _t−_ 1<sup>.Frequencybinsaredefinedfor</sup><sup>_n_=0,1,2,3-5,</sup> 6-10, 11-100 and _>_ 100 shipments in the year prior to the inspection decision. The dummy variable indicating observations with 0 lagged shipments is omitted from the regression. The lagged inspection rate, unit value, _ad valorem_ tariff and multiple goods variables control for variation in expected risks/harms. Standard errors are clustered by Product _×_ Origin Country and reported in brackets. The symbols ***,**,* represent significance at the 1%, 5%, and 10% level.

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in inspection rates are fairly large when one considers that the aggregate inspection rate in 2016 was 7 _._ 3 inspections per 100 shipments. Even after conditioning for a shipment type’s country of origin and HS10 product, infrequently observed types were inspected considerably more often than those that appear regularly at the border.

In column 2 we include a continuous measure of lagged shipment frequency. The coefficient on the continuous variable is also negative and statistically significant. This result offers further evidence that lagged shipment frequency and the inspection rate are inversely correlated. The inclusion of the continuous lagged shipment frequency variable reduces the coefficient on the larger frequency bins more than on the bins with fewer shipments, as would be expected.

In column 3 we include a vector of variables that are intended as controls for the underlying riskiness of the shipments. The coefficient on the lagged inspection variable indicates that shipments that were inspected in 2015 were more likely to be inspected in 2016. Shipments with higher unit values were less likely to be inspected.<sup>29</sup> The coefficient on the _ad valorem_ tariff variable is not statistically significant, which is not surprising given our inclusion of product-origin country fixed effects.<sup>30</sup> Finally the multiple goods variable is positive and statistically significant as expected.

In column 4, we add an importing-firm fixed effect. The estimated coefficients all retain the same signs, but the magnitudes are reduced considerably. The risk variables that were significant in column 3 remain significant. The lagged shipment frequency bins continue to be negative and significant, but the continuous measure of lagged shipment frequency is no longer significant in this specification.

In columns 5 and 6 we estimate a pooled regression over shipments from 2013 to 2016.

> 29Low priced goods may be seen as inspection risks because declaring low prices is a tariff evasion strategy. Lower prices may also indicate lower quality, which could be correlated with product safety and other risks. Note that all specifications include product-origin country fixed effects, so these estimates are identified solely off of variation in unit values across firms, but within product-origin country pairs.

> 30Most variation in duties occurs at the product-origin country level, and is swept out by the fixed effects. There is some within- _ofk_ variation in duties paid in these data. The Serbian customs agency charges interest on duties that are not paid promptly, and these interest payments are recorded as part of the duties paid. This generates variation within _ok_ pairs, but our results show that such variation is not quantitatively significant in terms of predicting inspection activity.

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Both specifications use product-origin country-year fixed effects in place of the product-origin country fixed effects used in the cross section. The coefficient estimates in column 5 are quite similar to the 2016 cross-section results in column 3. In column 6 we add importing firm-year fixed effects, and find similar coefficients to those reported in column 4, which used the 2016 cross-section alone.

Overall, we find that the relationship between the inspection rate and lagged shipment frequency is robustly negative, and sizably so when we allow variation across importing firms to drive the estimates. Our estimates do not allow us to rule out an alternative explanation for this conditional correlation: the Serbian customs agency may inspect infrequentlyobserved shipment types more often because shipments that are rarely seen are less likely to comply with import regulations. While it is quite plausible that compliance is related to frequency, we think it unlikely that this explains entirely the large negative effects we estimate in specifications without an importing-firm dummy. In our view, the sizable reduction in the estimated effect of frequency on inspection rates that occurs when importing-firm fixed effects are included in the specification also points to a role for ambiguity - the agency is not likely to have fully formed priors about the expected compliance of firms that import infrequently. Sweeping out cross-firm variation will tend to sweep out variation in the ambiguity attached to the agency’s expectation of each firm’s compliance probability. Ultimately, our focus on ambiguity depends not only on our empirical results, but also on discussions with operational experts, experts who view the inspection of new or rarely observed import shipment types as informational.

# **4 Model**

In this section we present a stylized model. Our approach to the theory is meant to illustrate the flexibility of the framework for application to different settings. In the numerical simulation in section 5, we choose a setting, functional forms and parameters that illustrate the operation of the model in a portion of the parameter space that is relevant to reform.

In the model shipments of traded goods arrive to the country’s border, and there are 18
risks associated with the goods in regard to health, safety and environment (from now on, HSE). To control these risks, the border inspection agency searches shipments of goods from time to time. We assume that each shipment is associated with a unique good and a unique importer. There is an upper bound on the maximum number of searches the agency can perform, which is given by _S_ .<sup>31</sup> When a search is performed, we assume that a noncompliant shipment is identified with probability 1. There is a continuum of shipments and each shipment can be categorized with respect to its observed characteristics, such as country of origin, transportation method, etc. For expositional purposes, assume that we have two mutually exclusive characteristics, say _A_ and _B_ .<sup>32,33</sup> Some shipments are in category _A_ , some are in category _B_ . As a result, we have a total of 2 groups, say 1 and 2 with measures _N_ 1 and _N_ 2, respectively. Throughout, index _l ∈{_ 1 _,_ 2 _}_ will denote the group.

There is a threshold level of compliance that must be satisfied. If a shipment is searched and found not to satisfy this compliance threshold, it cannot enter the country and the importer incurs a loss of $ _L >_ 0.<sup>34</sup> We assume that importers can secure the satisfaction of this threshold by incurring some cost that depends on their shipments’ particulars. Let _c_ ( _y_ ) represent the cost required for a shipment with particulars _y_ . We assume that _c_ ( _._ ) is invertible and _c_<sup>_′_</sup> _>_ 0 and _y_ is a realization of a random variable _Yl_ with the cdf of _Fl_ and pdf of _fl_ for _l ∈{_ 1 _,_ 2 _}_ . Thus, we allow the distribution of shipments’ particulars to differ across groups. Moreover, both _Yl_ ’s are non-negative, and their supports include zero. A shipment’s particulars, hence compliance cost, is unobservable to the border inspection agency. On the other hand, given the shipment’s characteristics, the inspecting agency can observe the group to which the shipment belongs.<sup>35</sup>

> 31One possible way to justify this assumption is to consider a case where a budget for search is limited. Alternatively, it can be due to a time constraint.

> 32There are different ways to interpret these characteristics. For example, _A_ may represent shipments from developing countries whereas _B_ may represent shipments from developed countries. Alternatively, _A_ may represent shipments of new importers while _B_ may represent shipments of seasoned importers.

> 33It is straightforward to generalize the model to any number of mutually exclusive characteristics.

> 34This loss can represent either the loss incurred by not entering the country or a fine charged for failing to comply. It can potentially vary from one shipment to another. We simply assume it to be constant since our results continue to hold as long as deterrence is not perfect.

> 35This setup can also be used to model a customs agency’s problem of minimizing the expected number of importers that misreport customs declarations. To see this, consider the following. There are tariffs imposed

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Denote _Sl_ the measure of searches of shipments in group _l_ . Denote with _sl_ = _NSll_<sup>the</sup> search intensity in group _l_ . _sl_ represents the probability that a random shipment in group _l_ is searched. As a result, we must have For a given search intensity, importers of each shipment decide whether to incur the cost to comply or not. They will comply _if and only if_ The function _c_<sup>_−_1</sup> ( _slL_ ) represents the expected benefit of compliance to the HSE standards when the search intensity is _sl_ and the loss of not satisfying the compliance standard is _L_ . Hence, for a given _sl_ and _L_ , the probability that a shipment in group _l_ does comply is given by _pl_ ( _sl_ ) _≡ Fl_ ( _c_<sup>_−_1</sup> ( _slL_ )). Given that _Fl_ is a cdf and _c_ ( _._ ) is an increasing function,<sup>36</sup> we have _p_<sup>_′_</sup> _l_<sup>(</sup><sup>_sl_)</sup><sup>_>_0.Inaddition,weassumethat</sup><sup>_p_</sup> _′′l_<sup>(</sup><sup>_sl_)</sup><sup>_<_0.</sup> The inspecting agency faces uncertainty (ambiguity) with respect to the compliance of shipments in each group. Under standard subjective expected utility theory (with subjective probabilities as in Savage, 1954), the agency assigns a probability distribution over the set of possible events and chooses an action from the available set to maximize its expected utility. However, this approach was challenged by the Ellsberg paradox (Ellsberg, 1961) in which people’s choices violate a postulate of subjective expected utility, the Sure-ThingPrinciple.<sup>37</sup> In contrast, here the inspecting agency has some belief about the compliance of shipments in each group, but lacks confidence in its belief. As a result, the agency may react

> on import shipments. Depending on its type, _y_ , the shipment can be a low tariff item or a high tariff item. Each importer declares its type and its tariff is determined accordingly. Assume that _c_ ( _y_ ) represents the benefit importer receives from understating its type. To prevent misreporting, the customs agency searches the content of import shipments to see whether their actual type matches with their declared type. After a search, if an importer is found to be misreporting, it incurs a loss of $ _L_ . There is a resource constraint on the maximum number of searches that can be performed, which is given by _S_ .

> 36 _′ −_ 1 _′_ Since _c >_ 0, we have _c >_ 0.

> 37According to the Sure-Thing-principle, if an individual takes a certain action when an event occurs as well as when it does not occur, then he/she should take the same action even if he/she does know nothing about that event’s occurrence. We can use an example of Ellsberg Paradox to show how this principle is

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to ambiguity by developing optimistic and pessimistic attitudes towards the compliance of shipments. While optimistic beliefs cause the overweighting of positive outcomes, i.e., compliance, pessimistic beliefs result in the overweighting of negative outcomes, i.e., noncompliance.

In order to model this ambiguity, we consider a specific type of capacity for the agency’s beliefs about compliance, a neo-additive (non-extremal-outcome-additive) capacity. A capacity is a normalized monotone set function that maps events to real numbers. A neo-additive capacity is a non-additive capacity that consists of a convex combination of an additive capacity,<sup>38</sup> and a special type of non-additive capacity that only distinguishes between whether an event is impossible, possible or certain, which is called Hurwicz capacity by Chateauneuf _et al._ (2007).<sup>39</sup> Non-additivity permits us to analyze different attitudes toward ambiguity.

Formally, we represent the inspecting agency’s belief about the likelihood of a shipment’s compliance in group _l_ with a neo-additive capacity _v_ based on _{pl,_ 1 _− pl}_ as where _δl_ , _αl ∈_ [0, 1] and we normalize _vl_ (0) = 0 and _vl_ (1) = 1. Similarly, the inspecting agency’s belief about the likelihood of non-compliance of any shipment in group _l_ is Note that in general _vl_ ( _pl_ ( _sl_ )) + _vl_ (1 _− pl_ ( _sl_ )) = 1, unless _δl_ = 0 or _αl_ = 2<sup><u>1</u>.</sup> violated. Consider two urns. In Urn 1, there are 5 red and 5 blue marbles. Urn 2 has 10 marbles with red and blue colors in unknown proportions. People engage in 2 gambles. In Gamble 1, they receive $20 if they draw a blue marble and nothing if they draw a red marble, whereas in Gamble 2, they receive $20 if they draw a red marble and nothing if they draw a blue marble. Each person can choose which urn to draw from. It turns out that most people choose to draw from Urn 1 in both gambles, which is inconsistent with the Sure-Thing-Principle. This is so since according to this principle, if one chooses Urn 1 for Gamble 1, then the same person must choose Urn 2 for Gamble 2 or _vice versa_ . For more on Ellsberg paradox and experimental evidence, see Camerer (1995).

> 38A capacity is additive when it is both concave and convex. Consider a capacity _v_ and 2 events _A_ and _B_ . Additivity implies

For example, probability distributions are additive.

> 39We consider only the empty set as impossible or null and only the whole state space as certain.

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The inspecting agency is assumed to have Choquet Expected Utility (CEU) preferences. The decision weights used in the computation of the Choquet integral will overweight better (worse) outcomes if the capacity is concave (convex). It is therefore well-suited to model such responses to ambiguity as optimism and pessimism. By using neo-additive capacity in the context of CEU framework, we can incorporate the inspecting agency’s optimistic and pessimistic attitudes towards uncertainty.<sup>40</sup> Given the inspecting agency’s beliefs in equations (1) and (2), its CEU (for a specific utility function based on the inspecting agency’s objective) of searching group _l_ with intensity _sl_ is where _M_ ( _sl_ ), _m_ ( _sl_ ), and _Epl_ ( _sl_ ) denote the maximum utility, the minimum utility and the expected utility with respect to _pl_ , respectively, of searching group _l_ with intensity _sl_ . The parameters _δl_ and _αl_ represent the agency’s ambiguity and the degree of optimism with regards to group _l_ , respectively. In plain words, ambiguity measures uncertainty about the underlying probability that a shipment in group _l_ is compliant with regulations. When facing ambiguity, the agency might have a positive (optimistic) or negative (pessimistic) attitude towards the compliance of shipments. Larger values of _δl_ and _αl_ correspond to higher degree of ambiguity and optimism, respectively.<sup>41</sup>

# **4.1 Minimizing expected non-compliance among** **_unsearched_ shipments**

We assume that the inspecting agency wants to minimize expected non-compliance among _unsearched_ shipments subject to its resource constraint. Since a search identifies a noncompliant shipment with probability one, shipments that go through search cannot cause any harm to the economy (because the inspection resolves the HSE risk). As a result, focusing search efforts to minimize non-compliance among _unsearched_ shipments also minimizes the

> 40In general, neo-additive capacities are neither convex nor concave. However, as shown by Chateauneuf _et al._ (2007), the ‘multiple-prior’ representation of neo-additive capacities allows a separation between ambiguity and attitudes towards ambiguity, i.e., pessimism and optimism.

> 41Further details of neo-additive capacity and the Choquet integral is provided in appendix B.

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HSE risk. We will use an asterisk (<sup>_∗_</sup> ) to denote equilibrium values and assume the existence of an interior solution.

Based on equation (3), the first task is to determine the maximum utility ( _M_ ( _sl_ )), minimum utility ( _m_ ( _sl_ )) and the expected utility ( _Epl_ ( _sl_ )) in accordance with this objective function. The maximum utility is obtained in the best case outcome in which if _Sl_ number of searches are performed in group _l_ , all of the remaining shipments which are not searched in group _l_ comply: On the other hand, the minimum utility is obtained in the worst case outcome where if _Sl_ number of searches are done in group _l_ , none of the remaining shipments which are not searched comply: Finally the standard expected utility with respect to _pl_ can be found as Substituting equations (4), (5) and (6) into equation (3) allows the objective function to be rewritten as The term in the square brackets shows the decision weight assigned to non-compliance. It consists of the weighted average of the degree of pessimism toward compliance and the expected probability of compliance, where the weights are based on the ambiguity parameter. The inspecting agency’s problem can be written as<sup>42</sup>

> 42Our model is static. In a dynamic setting, one can examine various extensions of this basic framework,

23
which is identical to the minimization problem given by the following Lagrangian Taking first order condition with respect to _sl_ , we obtain<sup>43</sup> where on the left-hand side, the first term in square brackets is the change in the proportion of unsearched shipments while keeping the decision weight on non-compliance constant, and the second term is the change in the decision weight on non-compliance of unsearched shipments while keeping their proportion constant. The former represents the direct effect of search in detecting non-compliant shipments, whereas the latter represents the indirect effect of search in discouraging non-compliant behavior among unsearched shipments.<sup>44</sup> The magnitude of this indirect effect critically depends on the agency’s uncertainty about the underlying probability distribution such that the more uncertainty there is (higher _δl_ ), the less will be the change through this indirect effect.

After some manipulation, the first order conditions with respect to _s_ 1 and _s_ 2 imply The equilibrium is determined according to equation (8) together with _N_ 1 _s_<sup>_∗_</sup> 1<sup>+</sup><sup>_N_2</sup><sup>_s∗_</sup> 2<sup>=</sup> _S_ .

Some observations are in order. First, when _δ_ 1 = _δ_ 2 = 0 (no ambiguity), then we have standard expected utility maximization with full confidence. The equilibrium is determined according to

> such as: (i) the trade-off between the best allocation of inspection rates for outcomes today and improving the accuracy of forecasts/beliefs for the future, and (ii) the updating of beliefs about compliance of shipments based on past compliance outcomes. While we thank anonymous referees for these interesting extensions, we believe that their analyses would require a separate study and thus beyond the scope of the current paper.

> 43Note that since _p′l_<sup>(</sup><sup>_sl_)</sup><sup>_>_0and</sup><sup>_p_</sup> _′′l_<sup>(</sup><sup>_sl_)</sup><sup>_<_0,thesecondorderconditionissatisfied.</sup>

> 44To draw a contrast between our paper and those of Knowles _et al._ (2001) and Persico (2002), if we were to analyze a single inspecting officer’s problem, this indirect effect would be absent since the single officer would not take into account the effect of his search effort on the compliance of unsearched shipments.

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together with _N_ 1 _s_<sup>_∗_</sup> 1<sup>+</sup><sup>_N_2</sup><sup>_s∗_</sup> 1<sup>=</sup> _S_ .

Second, when _δ_ 1 = _δ_ 2 = 1 (full ambiguity), if _αi < αj_ then we have _s_<sup>_∗_</sup> _i_<sup>=</sup> _NSi_<sup>and</sup><sup>_s∗_</sup> _j_<sup>= 0.</sup> In case _α_ ’s are identical, we have infinitely many equilibria such that any _s_<sup>_∗_</sup> _l_<sup>_∈_[0</sup><sup>_,_</sup> _NSl_<sup>]canbe</sup> 2 equilibrium as long as � _Nlsl_ = _S_ . In other words, all search effort is directed towards the _l_ =1 group in which the agency is relatively more pessimistic.

Third, if we assume _F_ 1 = _F_ 2, _α_ 1 = _α_ 2 and _δ_ 1 = _δ_ 2 _<_ 1, then we obtain _s_<sup>_∗_</sup> 1<sup>=</sup><sup>_s∗_</sup> 2<sup>.</sup>

# **4.2 Comparative Statics**

Consider equation (8), where _s_ 2 = _<u>S−NN</u>_ 21 _<u>s</u>_ <u>1</u> . A closer look at this expression shows us that _∂s_<sup>_∗_</sup> _<u>i</u>_<sup>0and</sup> _∂s_<sup>_∗_</sup> _<u>j</u>_<sup>0.Thismeansthesearchintensityofgroup</sup><sup>_i_increases(whilethatof</sup> _∂αi_<sup>_<_</sup> _∂αi_<sup>_>_</sup> group _j_ decreases) whenever the inspecting agency becomes less optimistic towards group _i_ . In addition, at _sl_ = _s_<sup>_∗_</sup> _l_<sup>wehave</sup> This condition implies that an increase in ambiguity of group _i_ increases (decreases) the search intensity of group _i_ , whenever the magnitude of the pessimism in the belief is larger (smaller) than the effect of a marginal increase in search intensity on the compliance of the proportion of unsearched importers. Intuitively, there are two opposing forces. On the one hand, for a given pessimistic belief about compliance of a group, an increase in ambiguity of that group calls for an increase in search intensity. On the other hand, search serves to discourage non-compliant behavior and as ambiguity increases for a particular group, this deterrent effect of searching shipments in that group becomes less relevant.<sup>45</sup> The result depends on which force dominates. Further, due to the binding resource constraint, as one group’s search intensity increases (decreases), the other group’s search intensity decreases (increases).

We can also look at what happens to the expected compliance of _unsearched_ shipments

> 45Search affects the probability of compliance, but more ambiguity means less confidence about the underlying probability distribution.

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when ambiguity decreases proportionally across groups. Assume that _F_ 1 and _F_ 2 are indeed the true distributions of groups 1 and 2, respectively. In that case, the optimal allocation of search intensity that minimizes expected non-compliance among _unsearched_ shipments is given by equation (9). If this equation is satisfied even in the presence of ambiguity, then it is not possible to improve the compliance further and a proportional reduction in ambiguity has no effect. Therefore, consider the scenario in which due to ambiguity, equation (9) does not hold. We can state the following proposition.

**Proposition** _Assume F_ 1 _and F_ 2 _are true distributions of groups_ 1 _and_ 2 _, respectively. A proportional decrease in ambiguity that leaves_<sup>_<u>δ</u>_</sup> _δ_<sup><u>1</u></sup> 2<sup>_constantimprovestheexpectedcompliance_</sup> _of unsearched shipments._

**Proof.** Dividing both sides of equation (8) by _δ_ 2, we have

As a result of an equal percentage decrease in _δ_ 1 and _δ_ 2, the first term on both sides of the equation does not change. The change can come from the difference in the relative magnitude of _I_ and _J_ terms, where _I >_ 0 and _J >_ 0 are defined in the above equation. We also know from equation (9) that expected non-compliance among _unsearched_ shipments is minimized when _I_ = _J_ . As we stated above, our focus is on cases in which _I_ = _J_ .

We need to show that a proportional decrease in ambiguity for both groups that leaves _<u>δ</u>_ <u>1</u><sup>brings</sup><sup>_I_and</sup><sup>_J_termscloser.Tothatpurpose,assumethat</sup><sup>_I> J_.Inthiscase,</sup> _δ_ 2<sup>constant</sup> following an equal percentage decrease in _δ_ 1 and _δ_ 2, holding _I_ and _J_ constant, the left-hand side of the equation (11) goes up more than the right-hand side of the same equation. To establish equality again, _I − J_ must go down. Notice that in the limit when ambiguity is completely eliminated, we have _I − J →_ 0. The analysis of _I < J_ follows similar steps. ■ 26
# **5 Calibration/Numerical simulation**

To illustrate the operation of the model in the portion of the parameter space that is most relevant for operational risk management reforms, we calibrate the model to Serbian data for 2016 and conduct counterfactual analysis. Because the model is calibrated to data from a system that uses modern risk management methods, our counterfactual is a _reverse_ reform; we increase both ambiguity and search. In order to better understand the quantitative contribution of each change to the system, we conduct the counterfactual in two steps. We first simulate the removal of advanced IT systems by substantially increasing ambiguity while holding fixed the aggregate number of searches. Increased ambiguity magnifies the misallocation of search activity and reduces aggregate compliance. In the second step, we raise the level of total search activity to the level that is necessary to restore aggregate compliance.

Although we calibrate to actual data on inspection activity, our calibration remains a stylized example. In an actual risk management reform, especially one occurring in a customs – – agency, there would be enormous heterogeneity across countries, products and firms in model parameters, and in observed outcomes.<sup>46</sup> In this calibration we shut down much of this variation. Shipment types differ only in their ambiguity parameters, which are determined solely as a function of the lagged shipment frequency of each type. The model is calibrated such that the agency inspects more frequently shipment types about which there is greater ambiguity. Variation in inspection rates generates endogenous variation across bins in the compliance rate.

In the computational model the agency solves the minimization problem in equation (7). Instead of two shipment types _l_ as in the theory, the computational model has seven, each corresponding to one of the lagged shipment bins in Table 1. The compliance cost function is _c_ ( _y_ ) = _y_ . Since _c_<sup>_′_</sup> ( _y_ ) = _y_ in this case, the compliance rate in each bin can be represented as _pl_ ( _sl_ ) _≡ Fl_ (( _slL_ )). We choose a Pareto distribution for _Fl_ and parameterize the distribution 46The non-customs agencies – for example those responsible for sanitary and phytosanitary standards – oversee a smaller range of products and, in some cases, one might expect less variation in their implied model parameters.

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as part of the calibration.

Consistent with the data, the inspecting agency is allowed 7 _._ 3 inspections per 100 shipments, which it allocates endogenously across the seven bins. Each bin’s share of total shipment activity matches that in column 2 of Table 1. The other parameters of the model are chosen to fit, as closely as possible, the distribution of inspection activity across bins. A parsimonious function constrains the parameters of interest; the _δl_ ’s vary inversely with lagged shipment frequency. In the interests of brevity we leave the calibration details to appendix C.

Table 3 reports the results of the calibration and the two counterfactual scenarios. Panel A reports details of the calibrated model in the benchmark equilibrium. As in Table 1, inspection activity in the data falls most heavily on shipments that were not observed in the previous period. By construction, the ambiguity parameters ( _δl_ ’s) fall with lagged shipment frequency.<sup>47</sup> Since we have parameterized the model to produce equal probabilities of compliance across bins – conditional on equal search rates – observed variation in inspection rates is solely an outcome of cross-bin variation in _δl_ . Importers respond to the variation in search intensity with different compliance rates. Compliance rates vary from 0 _._ 993 to 0 _._ 982. In aggregate, the compliance level in the benchmark is 0 _._ 985.<sup>48</sup> Panel B shows equilibrium rates of inspection and compliance after the first step of counterfactual analysis, a tripling of _δl_ in each bin. In the bin with zero lagged shipments, _δl_ rises nearly to 1, and the agency shifts much of its inspection activity towards mitigating the high level of ambiguity in this bin. Since the aggregate inspection rate stays fixed at

> 47In calibrating the model we impose a monotonically decreasing function that relates _δl_ to lagged shipment frequency in bin _l_ . Panel A of Table 3 shows that in the data, the inspection rate for the final lagged shipment frequency bin lies above those of the two preceding bins, though not substantially so. It is likely that factors other than ambiguity are driving this somewhat higher inspection rate among the most frequently shipped goods. In the calibrated model, the bin with the most frequently observed shipments has the lowest value of _δl_ and the lowest benchmark inspection rate.

> 48We have no direct data on compliance levels in Serbian customs. This is a model outcome. The World Bank working paper version of Fernandes _et al._ (2021) reports information on penalties assessed by Albanian customs in 2007, and finds that penalties were assessed on only 132 of 178 _,_ 639 shipments, or 7 _/_ 100ths of one percent. Konar Leacy _et al._ (2019) report positive tests in 6.1 percent of tested shipments after reform in a technical agency focused inspection on the riskiest shipments. In light of these results, we view an aggregate compliance rate of 98 _._ 5 percent as a reasonable benchmark.

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Table 3: Calibration and simulation results

|Lagged shipment frequency bin|0|1|2|3-5|6-10|11-100|100+|
|---|---|---|---|---|---|---|---|
|**Panel A. Benchmark Calibration**||||||||
|Inspections per 100 shipments (data)|14|6.7|6.4|6.0|5.6|5.7|6.0|
|Inspections per 100 shipments (ftted)|13.9|6.8|6.3|6.0|5.8|5.6|5.6|
|Ambiguity (_δl_)|0.330|0.165|0.110|0.069|0.038|0.012|0.002|
|Compliance rate per bin _p_(_s_<sup>_∗_</sup><br>_l_ <sup>)</sup>|0.993|0.985|0.984|0.983|0.983|0.982|0.982|
|Aggregate compliance rate||||0.985||||
|Total inspections per 100 shipments||||7.3||||
|**Panel B. Removing IT; threefold **|**increas**|**e in** _δl_||||||
|Inspections per 100 shipments|24.1|3.4|3.4|3.4|3.4|3.4|3.4|
|Ambiguity (_δl_)|0.990|0.495|0.330|0.206|0.115|0.035|0.005|
|Compliance rate per bin _p_(_s_<sup>_∗_</sup><br>_l_ <sup>)</sup>|0.996|0.971|0.971|0.971|0.971|0.971|0.971|
|Aggregate compliance rate||||0.975||||
|Total inspections per 100 shipments||||7.3||||
|**Panel C. Restore compliance with**|**increa**|**sed sea**|**rch**|||||
|Inspections per 100 shipments|100|37|6.7|5.6|5.1|4.9|4.8|
|Ambiguity (_δl_)|0.990|0.495|0.330|0.206|0.115|0.035|0.005|
|Compliance rate per bin _p_(_s_<sup>_∗_</sup><br>_l_ <sup>)</sup>|0.999|0.997|0.985|0.982|0.981|0.980|0.979|
|Aggregate compliance rate||||0.985||||
|Total inspections per 100 shipments||||24.5||||

Table notes: Key outcomes in the calibrated benchmark, and in the two-step counterfactual analysis. Data are organized by the lagged shipment frequency bins previously outlined. Panel A reports the outcomes of the model in the calibrated benchmark. The key fitted outcomes are the _δl_ parameters, which allocate inspection activity across bins, and thus compliance rates. Panel B reports equilibrium rates of search and compliance after a tripling of the _δl_ parameters. The scenario reported in Panel C identifies the level of aggregate search activity that restores compliance to its benchmark level. Panel C also reports the allocation of search activity and bin-specific compliance rates for that scenario.

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7 _._ 3 inspections per 100 shipments, the rise in inspections in the first bin requires offsetting reductions in inspection activity in the other six bins. Compliance in the other bins falls along with reduced inspection rates, causing the aggregate compliance rate to fall to 0 _._ 975.

We do not produce a quantitative estimate of the welfare costs of increased ambiguity, because we lack direct evidence on a key parameter, the social harm from non-compliant goods that enter the country. Given a measure of the social loss per non-compliant shipment, calculating the welfare loss at this stage would be straightforward. The one percentage point reduction in aggregate compliance should be multiplied by the total number of import shipments, and by the social loss per non-compliant shipment.<sup>49</sup> We next turn to the second step of the counterfactual analysis. In this step we hold fixed the ambiguity levels, but raise the total number of searches, _S_ . Aggregate search levels are raised until the aggregate compliance rate matches its initial level of 0 _._ 985. The results of this exercise are reported in Panel C. The rise in aggregate search increases equilibrium search intensity in each bin, but search intensity rises more in the bins with higher levels of ambiguity. Increased search intensity improves compliance.

The key result from the second step of the counterfactual analysis is that restoring aggregate compliance requires aggregate search activity to rise from 7 _._ 3 to 24 _._ 5 inspections per 100 shipments. To hold compliance rates fixed, a tripling of ambiguity requires a 236 percent increase in total searches of import shipments. Conversely, the model suggests that a reform that reduced ambiguity by 66 _._ 7 percent could reduce overall search intensity by 70 _._ 2 percent without affecting compliance.<sup>50</sup> Because the increased search intensity has restored levels of aggregate compliance, the nature of the welfare loss due to increased search takes a different form than that resulting

> 49Since trade flows are exogenous in the model, there is no welfare loss and/or gain from changes in trade flows. In this case there are no net changes in total search activity, only shifts of search intensity across bins. Changes in the aggregate trade flow would depend on differences across bins in the sensitivity of trade to inspections. In the case of the Albanian customs reform, Fernandes _et al._ (2021) Tables 4-6 show that inspections have a stronger effect on less frequent shipments than on more frequent shipments.

> 50Reductions in search intensity of this magnitude have been observed in the literature. The risk management reform in Albania studied by Fernandes _et al._ (2021) saw the intensity of ‘red channel’ searches fall from 42 _._ 9 percent in 2007 to 11 _._ 2 percent in 2012, a 73 _._ 9 percent reduction.

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from increased ambiguity. In this case, the first order loss can be calculated as the change in search intensity (0 _._ 245 _−_ 0 _._ 073 = 0 _._ 172) multiplied by the cost of conducting a search multiplied by the total number of import shipments. We lack direct evidence on the size of the search cost per shipment. Yet assuming that the cost of search is 1 percent of the value of the goods, the welfare cost of increased search is a tariff-equivalent trade cost of 0 _._ 172 percentage points.<sup>51</sup> It is also likely that increased search would reduce trade volumes, causing additional welfare losses.

# **6 Conclusion**

An ideal trade facilitation reform should accomplish two objectives that might otherwise seem to be in conflict: It should decrease the overall oversight burden on trading firms – – while improving upon or at least maintaining existing levels of compliance. We have demonstrated how risk management reforms that include the adoption of modern IT systems might jointly achieve both objectives. We argue that a fundamental problem in the oversight of imported goods shipments is that the enormous variety of products, countries of origin, trading firms and compliance risks makes it extremely difficult for oversight agencies to make an informed assessment of the _ex ante_ probability that a given shipment is a noncompliance risk. This ambiguity about expected probabilities of non-compliance often means that developing country border management agencies conduct too many inspections, and do a poor job of targeting inspections. Modern IT systems are instrumental in reducing ambiguity, and are thus a critical component of the trade facilitation reform known as risk management.

To illustrate the difficulty of managing risks in this environment, we show that a sizable majority of import shipment types observed by Serbian customs were observed rarely in the previous year, if at all. The preponderance of shipments without a recent compliance record poses a challenge for a system that relies, operationally, on conditional forecasts of

> 51Note that in contrast to a tariff, this trade cost generates no tax revenue. Additional search imposes real resource costs, so the welfare loss is significantly larger than from an equivalent tariff that raises revenue.

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compliance at the level of individual shipments. We show that the agency inspects infrequent shipments more often than other shipments, even after controlling for available indicators of underlying risk. We argue that this behavior likely represents a response to ambiguity about expected compliance rates among infrequently observed shipments.

We formalize these insights using a tractable form of a Choquet Expected Utility framework that represents ambiguity with a single parameter. Under our assumed objective function, search plays two roles: detecting non-compliant shipments and discouraging noncompliant behavior on unsearched shipments. The presence of ambiguity unsettles the inspecting agency’s belief about the efficacy of the discouraging role of search. The agency that is pessimistic about compliance reacts by increasing search on those shipments in which there is more ambiguity. Both our empirical evidence and discussions with operational experts support this view: inspecting agencies mitigate ambiguity with additional search.

We develop a quantitative model to illustrate, numerically, the role of ambiguity in a realistic parameterization of the distribution of search activity and firm-level compliance. Counterfactual changes in ambiguity - which are plausibly attributable to IT - change the distribution of search activity and the level of search activity needed to maintain compliance. Our results are indicative of the kinds of benefits that accrue to countries that successfully implement risk management in their border inspection agencies.

# **Appendix A: Summary statistics**

Summary statistics for the 2013-16 data are presented in Table 4. The mean annual number of import shipments per combination of product, origin country, and importing firm is 5 _._ 55 and the mean number of inspections per triplet is 0 _._ 40. The mean observation was inspected 7 _._ 8 times per 100 shipments. 54 percent of _ofk_ triplets had not been observed in the previous year. The mean observation saw 4 _._ 23 lagged shipments in the previous year.

Among the risk control variables, we see that the mean lagged inspection rate is 3 percent and the average logged unit value is 7 _._ 77 (Serbian dinars per kilogram). The mean _ad valorem_ tariff is 7 _/_ 100ths of one percent. The very large maximum value for this variable reflects the 32
inclusion of interest on late payment of duties. The multi-goods variable, which measures the average number of products on declarations containing each _ofkt_ observation, has a mean of 7 _._ 53. One declaration contained 212 HS10 products.

Table 4: Summary Statistics for 2013-16

||N|Mean|SD|Min|Max|
|---|---|---|---|---|---|
|Shipments|2431641|5.55|22.02|1.00|5848.00|
|Inspections|2431641|0.40|5.64|0.00|2453.00|
|Inspection rate|2431641|7.80|24.72|0.00|100.00|
|Bin_n_=0|2431641|0.54|0.50|0.00|1.00|
|Bin_n_=1|2431641|0.13|0.33|0.00|1.00|
|Bin_n_=2|2431641|0.08|0.26|0.00|1.00|
|Bin_n∈_[3_−_5]|2431641|0.11|0.31|0.00|1.00|
|Bin_n∈_[6_−_10]|2431641|0.06|0.25|0.00|1.00|
|Bin_n∈_[11_−_100]|2431641|0.08|0.27|0.00|1.00|
|Bin_n>_100|2431641|0.00|0.07|0.00|1.00|
|Shipments_t−_1|2431641|4.23|19.94|0.00|5848.00|
|Insp_t−_1|2431641|2.98|14.53|0.00|100.00|
|ln UV_t_|2431615|7.77|2.08|-6.93|22.80|
|AV tarif_t_|2431641|0.07|9.13|0.00|8612.07|
|Multi-goods|2431454|7.53|11.57|1.00|212.00|

Table notes: Summary statistics for Serbian customs data from 2013-16. Annual data organized at the level of HS10 product, origin country and importing firm. _Bin_ variables are dummy variables indicating the frequency of shipments in the product-country-firm triplet in the previous year. Subscripts on the bin dummies indicate ranges of the number of lagged shipments associated with the dummy variable for that bin.

# **Appendix B: Theoretical framework**

## **General Framework**

It is assumed that the inspecting agency’s uncertainty can be described by a non-empty finite set of states, Γ. There is a set of events, _ε_ , associated with the set of states, which are the power set of Γ. It is assumed that for each _γ_ in Γ, _{γ}_ is in _ε_ . Let _X ⊂_ R be a non-empty, finite set of outcomes and let _G_ = _{g_ : Γ _→ X}_ be a simple set of functions from 33
states to outcomes, called simple acts. Let _U_ : _X →_ R be a monotone increasing function from outcomes to real numbers.

_Definition of Capacity_ . A capacity is a function _μ_ : _ε →_ R which assigns real numbers to events such that (i) _D_ , _E ∈ ε_ and _D ⊆ E_ implies _μ_ ( _D_ ) _≤ μ_ ( _E_ ) (monotonicity), and (ii) _μ_ (∅) = 0 and _μ_ (Γ) = 1 (normalization).

Note that a probability distribution is a special case of a capacity that satisfies additivity: _D_ , _E ∈ ε_ and _D ∩ E_ = ∅ implies _μ_ ( _D_ ) + _μ_ ( _E_ ) = _μ_ ( _D ∪ E_ ).

_Definition of Choquet Integral_ . Let _g_ : Γ _→ X_ be a simple act that takes on the values _x_ 1 ⩾ _x_ 2 ⩾ _..._ ⩾ _xn_ . The Choquet integral of _g_ with respect to a capacity _μ_ is defined as The Choquet integral can be interpreted as the expected value of the simple act _g_ with respect to the capacity _μ_ . The Choquet integral of the composition _U_ ( _g_ ( _γ_ )) with respect to the capacity _μ_ is defined as the Choquet Expected Utility of _g_ with respect to _μ_ . Note that the composition _U_ ( _g_ ( _γ_ )) : Γ _→_ R is a simple act.

A neo-additive capacity is a special type of capacity that is based on a probability distribution.

_Definition of Neo-additive Capacity_ . Let _α_ and _δ_ be real numbers such that 0 _≤ δ ≤_ 1 and 0 _≤ α ≤_ 1. A neo-additive capacity _v_ based on a probability distribution _π_ is defined as A neo-additive capacity is additive on non-extreme outcomes. Here, _π_ represents the agent’s beliefs about the likelihood of uncertain events, and 1 _− δ_ represents the agent’s degree of confidence in this belief. The complement of the degree of confidence is the degree of ambiguity _δ_ .

The Choquet integral of a simple act _g_ with respect to a neo-additive capacity _v_ based 34
on _π_ is given by (see Chateauneuf _et al.,_ 2007) where _g_ takes on the values _x_ 1 ⩾ _x_ 2 ⩾ _..._ ⩾ _xn_ . Therefore, with respect to a neo-additive capacity, the Choquet integral of a simple act _g_ is the weighted sum of the best outcome under _g_ , the worst outcome under _g_ , and the expected value of _g_ with respect to _π_ .

It follows that the Choquet Expected Utility of the simple act _g_ with respect to the neo-additive capacity _v_ based on _π_ is given by _n_ where _Eπ_ ( _g_ ) _≡_ � _U_ ( _xi_ ) _.π_ ( _{γ ∈_ Γ _| U_ ( _g_ ( _γ_ )) = _U_ ( _xi_ ) _}_ ). That is, it is the weighted sum of the _i_ =1 maximum utility under _g_ , the minimum utility under _g_ , and the expected utility of _g_ with respect to _π_ . In the above integral, _α_ can be interpreted as the degree of optimism and 1 _− α_ as the degree of pessimism since they are weights given to the maximum and the minimum utility, respectively. Notice when no ambiguity exists, the Choquet Expected Utility reduces to expected utility.

# **The Current Model**

The state space is Γ = _{_ compliance, non-compliance _}_ . The outcome space is _Xl_ = _{M_ ( _sl_ ) _, m_ ( _sl_ ) _}_ , where _M_ ( _sl_ ) = 0 and _m_ ( _sl_ ) = _−Nl_ (1 _− sl_ ). The set of acts _G_ = _{g_ ( _sl_ ) : _sl_ ⩾ 0 _}_ , where The inspecting agency’s utility function is _U_ ( _g_ ( _sl_ )) = _g_ ( _sl_ ).

The inspecting agency’s beliefs about the HSE risk are given by a neo-additive capacity based on the probability distribution _πl_ = _{pl_ ( _sl_ ) _,_ 1 _− pl_ ( _sl_ ) _}_ . Define _v_ ( _p_ ) := _v_ (compliance), _v_ (1 _− p_ ) := _v_ (non-compliance), and _Vpl_ ( _sl_ ) := _Vpl_ ( _g_ ( _sl_ )). Moreover, define _Epl_ ( _sl_ ) := _pl_ ( _sl_ ) _M_ ( _sl_ ) + (1 _− pl_ ( _sl_ )) _m_ ( _sl_ ). It follows that the inspecting agency’s Choquet Expected Utility of searching a random shipment from group _l_ with intensity _sl_ is _Vpl_ ( _sl_ ) = _δlαlM_ ( _sl_ )+ _δl_ (1 _− αl_ ) _m_ ( _sl_ ) + (1 _− δl_ ) _Epl_ ( _sl_ ).

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# **Appendix C: Calibration details**

In section 3 we observed a negative relationship between inspection rates and lagged shipment frequency. Under our working hypothesis that lagged shipment frequency is an inverse proxy for ambiguity, our model can produce this negative relationship for certain parameterizations. This appendix details the process of calibration used to generate the calibrated benchmark equilibrium.

The agency’s goal is to minimize the HSE risk (and, equivalently, minimize expected noncompliance among _unsearched_ shipments). We offer a brief restatement of the model using this framework. The Lagrangian associated with the optimization of the objective function is given by equation (7). A key variable in this expression is the probability of compliance _pl_ ( _sl_ ) _≡ Fl_ ( _c_<sup>_−_1</sup> ( _slL_ )). Numerical solution of the equilibrium requires assumptions about the underlying distribution of the attribute of shipments in each bin, _Fl_ , as well as the attributedependent costs of compliance, _c_ ( _y_ ). We begin by assuming a functional form for compliance costs: _c_ ( _y_ ) = _y_ , where attribute _y_ is a realization of a random variable _Yl_ with the cdf of _Fl_ and the pdf of _fl_ . This functional form implies _c_<sup>_−_1</sup> ( _y_ ) = _y_ and hence _p_ ( _sl_ ) _≡ Fl_ ( _slL_ ). In our numerical exercise, we assume that the attribute of shipments follows an identical distribution across bins. In particular, we simulate our model using the Pareto distribution with a scale parameter of _b_ and shape parameter of 1. The equations for _pl_ ( _sl_ ) and _p_<sup>_′_</sup> _l_<sup>(</sup><sup>_sl_)</sup> thus take the form: For purposes of accounting we add another equation to the model that keeps track of compliance across the entire system: The numerator of this expression is the sum over the number of compliant shipments in each bin, and the denominator is the sum over the number of shipments in each bin.

Equilibrium values of _sl_ are continuous rates, and are not required to be chosen to imply 36
a discrete number of inspections in each bin. We do not interpret _N_ as the literal number of shipments, but rather a representation of relative sizes of the number of shipments within each bin.<sup>52</sup> The values of _sl_ and _pl_ should therefore be interpreted as continuous rates. Equations (7), (12) and (13) define the computational model used in our exercises.<sup>53</sup>

# **Data summary**

We report the data that we seek to replicate in Table 5. Using the lagged shipment frequency bins we defined in section 3, we calculate key summary statistics from the 2016 data, statistics that we seek to match in our numerical model. The summary statistics we calculate are: (1) the total share of 2016 shipments in each bin, (2) the number of inspections conducted per 100 shipments in each bin, (3) the average number of lagged shipments (across product-country-firm combinations) in each bin, and (4) the number of inspections per 100 shipments in aggregate.<sup>54</sup> In aggregate, the inspection rate in 2016 was 7 _._ 3 inspections per 100 shipments. The key lesson from Table 5 is that the inspection rate is much higher for shipments that were not observed in the previous year (14 percent of shipments) than for shipments in the other six bins. Inspection rates fall sharply with lagged shipment frequency in the bins with fewer lagged shipments, and then rise somewhat for bins with larger shipment frequencies.<sup>55</sup> Also important for calibration are the bins’ shares of overall shipment activity. Trade flows are exogenous in our model, and we match all of the shipment bin weights exactly in our model calibration. We also calculate the mean number of lagged shipments per bin, a numerical value we use in calibrating ambiguity. The first three lagged shipment bins are

> 52We normalize the total number of shipments _N_ to 100, and allocate shipments across bins according to their proportions in the data.

> 53We solve this constrained optimization program using the GAMS software.

> 54As in the econometric estimates we report, inspections are defined broadly, notably including documentary inspections.

> 55The non-monotonicity in inspection rates across bins likely reflects variation across bins in the riskiness of the shipment types in each bin. The monotonic and decreasing progression of regression coefficients in most columns of Table 2 suggests a consistent inverse relationship between lagged shipment frequency and conditional inspection rates. In an earlier draft, we defined shipments at the HS6 level and observed a monotonic pattern in the unconditional inspection rates as well. We focus here on the sharp drop-off of inspection rates at low frequencies, as these are central to the problem.

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Table 5: Data to be calibrated

|Frequency of lagged shipments in bin|0|1|2|3-5|6-10|11-100|100+|
|---|---|---|---|---|---|---|---|
|Share of total 2016 shipments|0.189|0.051|0.038|0.084|0.089|0.374|0.176|
|Inspections per 100 shipments|14|6.7|6.4|6.0|5.6|5.7|6.0|
|Mean no. of lagged shipments|0|1|2|3.8|7.6|26.9|205|
|Total inspections per 100 shipments||||7.3||||

Table notes: Author calculations using Serbian customs data from 2016.

made up entirely of observations with exactly zero, one, or two lagged shipments, respectively. In the last four bins, we average over _ofk_ triplets that have varying levels of lagged shipment frequencies. The mean for each bin is reported in row 3 of Table 5.

# **Parameterization**

In order to emphasize the role of ambiguity, we shut down by assumption other possible sources of cross-bin variation that might otherwise affect search behavior and/or compliance. We restrict the optimism parameter to be equal across bins, _αl_ = _α_ , _∀l_ . Likewise the firm’s loss parameter, _L_ , is assumed to be common across bins.

The parameter _L_ represents the loss to the importer from having non-compliant goods seized by the border authority. This parameter can be important in determining overall levels of compliance, and our model fits best with generally high levels of compliance. In our exercise we set _L_ = $200.<sup>56</sup> We also choose the Pareto distribution scale parameter to generate relatively high levels of aggregate compliance; _b_ = 1.<sup>57</sup> The magnitude of the loss parameter is most relevant for the cost of compliance since their relationship determines the compliance decision of the importer.<sup>58</sup> Therefore, it is

> 56 The right-hand side of inequality (14) is decreasing in both _sl_ and _L_ (recall _p_ ( _sl_ ) _≡ F_ ( _slL_ )). With the relatively low levels of search activity observed in Serbian customs (which results in low levels of search intensity), we need a high level of _L_ for the calibration to satisfy inequality (14). In other words, we need to have high levels of compliance with low levels of search activity, which can be achieved with a hefty non-compliance cost.

> 57In an earlier draft of the paper, we set _b_ = 0 _._ 01 and _L_ = 10. these are both scale parameters, and any ratio of _b/L_ that is constant produces the same model outcomes. We choose to set _b_ = 1 here for clarity on some subsequent calculations.

> 58Note that if the loss parameter is related to the value of goods, the relationship between the loss parameter and the cost of compliance also _implicitly_ defines the relationship between the value of goods and the cost of compliance.

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appropriate to compare this loss value to the median cost of compliance to get a sense of its proportion. Our specifications imply that the median cost of compliance is $2, which makes the importer’s loss 100 times larger than the median cost of compliance.<sup>59</sup> Equation (12) implies that if 5 in every 1000 shipment were searched, no-one would comply, whereas if 10 in every 1000 shipment were searched, 50 percent of shipments would be compliant. We parameterize the model in a such a way that which ensures that bins with greater ambiguity will be searched more intensively in equilibrium (see equation (10)). The low levels of search activity in Serbian customs means that _sl_ is generally small, and _p_<sup>_′_</sup> ( _s_<sup>_∗_</sup> _l_<sup>)large.Thismeansthat</sup><sup>_α_cannotbetoolargeifinequality</sup> (14) is to hold. We choose _α_ = 0 _._ 13, a parameterization that implies moderate pessimism on the part of border officials.

Our key calibration target is the allocation of search activity across the seven shipment frequency bins. The structural parameters that determine these outcomes are the bin level ambiguity parameters, _δl_ ’s. To calibrate these parameters, we specify a parsimonious functional relationship between _δl_ and _N_<sup> ̄</sup> _l,t−_ 1, the mean lagged shipment frequency for that bin in the 2016 Serbian data. Our functional representation is where _γ_ is a calibration parameter.<sup>60</sup>

# **Equilibrium solution in the benchmark**

The primary targets in our calibration exercise are the inspection rates that were observed for each bin, which we reported in Table 5 and reproduced in the first row of Table 3, Panel A. In our calibration, each bin has the same share of overall shipments as was reported in Table

> 59For the median cost of compliance, we must have Pr ( _Y_ ⩽ _y_ ) = <u>12</u><sup>,thatis,1</sup><sup>_−_</sup> _y_<sup>_<u>b</u>_=</sup><sup><u>1</u></sup> 2<sup>.Plugging</sup><sup>_b_=1</sup> gives us the result.

> 60We experimented with other linear and simple non-linear functional forms, and found that equation (15) performed the best.

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5. We also impose the same aggregate search rate as was reported there, 7 _._ 3 inspections per 100 shipments. Given these restrictions and the parameter choices discussed in the previous subsection, we choose the value of _γ_ in equation (15) to best match the inspection rate targets.<sup>61</sup> A value of _γ_ = 0 _._ 33 aligns the inspection rates across bins reasonably well. We focus the calibration on hitting the very high levels of inspection activity on the first bin, and the drop-off that occurs over the other bins with few lagged shipments. We approximate the inspection frequency pretty well in all bins except the bin with the highest lagged frequency. The structural parameters that drive variation in the inspection rates across bins are the _δl_ ’s, all seven of which are pinned down by _γ_ and equation (15). Panel A of Table 3 reveals values of _δl_ that drop rapidly across shipment frequency bins. The ambiguity level for shipments that were not observed in the prior year is nearly an order of magnitude higher than the level observed for shipments occurring 6-10 times, and more than two orders of magnitude larger than the value of _δ_ that applies to the bin with shipments observed more than 100 times in the prior year.

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> 61Experimentation showed that increases in the optimism/pessimism parameter _α_ change the allocation of search activity in a manner similar to decreases in _γ_ . Relative to an earlier version of the paper, this parameterization has a larger value of _α_ , the effects of which are largely offset by somewhat larger _γ_ . These offsetting changes in the structural parameters had very little effect on the magnitude of the counterfactual changes in the model.

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