Smuggling illegal versus legal goods across the U.S.-Mexico border: a structural equations model approach.

Buehn, Andreas ; Eichler, Stefan

1. Introduction

In this article, we study smuggling across the U.S.-Mexico border from 1975 to 2004. We contribute to the literature in the following ways: First, we treat smuggling as an unobservable variable. Using a Multiple Indicators Multiple Causes (MIMIC) model we capture the latent nature of smuggling and identify its determinants and long run trends.1 Secondly, we argue that the analysis of smuggling has been incomplete so far; existing studies merely analyze the causes of trade misinvoicing--illegal trade or smuggling of legal goods--which represent only a fraction of total illegal trade. To improve the understanding of illegal trade, we distinguish between smuggling illegal goods versus smuggling legal goods.

The types of smuggling differ with respect to the goods being smuggled, the agents involved in smuggling, the smuggling incentive, and the intensity of law enforcement. Trade misinvoicing occurs when entrepreneurs misreport the value of legal exports or imports to evade tariffs and taxes and is commonly considered a peccadillo: Smugglers usually bribe officials or are fined a fee. Smuggling illegal "freight" such as illicit drugs and illegal immigrants, however, often involves dangerous criminals who commit serious offenses and who, if caught, face severe punishment. As a result, their incentive to smuggle is related to the intensity of law enforcement rather than tax or tariff evasion.

Studying the U.S.-Mexican case is appropriate, as most illegal drugs and immigrants enter the United States via the Mexican border. The large income disparity between the two nations may explain the high U.S. demand for illegal goods, which relatively poor Mexicans are willing to meet despite the risks involved. We examine whether the Clinton and Bush Administrations succeeded in reducing smuggling across the border through intensified border enforcement.

Using a simple microeconomic framework, we determine which microeconomic incentives affect the two types of smuggling. The hypotheses are then tested in a MIMIC model that studies the impact of observed causes (the microeconomic incentives to smuggle) on the latent phenomenon, smuggling, as indicated by observable macroeconomic variables. Applying the benchmarking procedure promoted by Dell'Anno and Schneider (2006) and Dell'Anno (2007), we calculate a time series for each type of smuggling. We find that smuggling in illegal goods from Mexico to the United States decreases when Mexican labor market conditions improve and U.S. border enforcement is intensified. The Mexican recessions in 1982-1983 and 1995 led to large temporary increases in smuggling to $113 billion and $87 billion, respectively. Smuggling in illegal goods decreased overall, however, from $116 billion in 1984 to $27 billion in 2004; this reduction can be attributed to stricter U.S. border enforcement and better Mexican job prospects.

Smuggling legal goods is driven by real exchange rates and tariff and tax evasion. Export misinvoicing fluctuated between underinvoicing values of $0.2 billion and overinvoicing values of $0.7 billion, while import misinvoicing switched from underinvoicing, peaking at $1.6 billion in 1983, to recent overinvoicing--up to $3.8 billion in 2002. This pattern can be attributed to substantial tariff reductions in accordance with the GATT in 1987 and the North American Free Trade Agreement (NAFTA) in 1994.

The rest of the article is organized as follows. Section 2 reviews the smuggling literature. Section 3 considers the incentives driving the two types of smuggling in a microeconomic framework. Section 4 explains the empirical methodology. Section 5 describes the indicators of smuggling. Section 6 presents the estimation results and long-term trends for the smuggling of illegal and legal goods. Section 7 concludes.

2. Literature

The existing smuggling literature focuses on trade misinvoicing, that is, the false declaration of legal imports and exports. One strand of the theoretical literature analyzes the welfare effects of trade misinvoicing. Bhagwati and Hansen (1973) show that despite the classic view, smuggling can distort welfare, as legal traders are squeezed out by smugglers who operate at inferior terms of trade but profit by circumventing tariffs. Pitt (1981) shows that the welfare consequences of smuggling are ambiguous. He argues that legal trade and smuggling coexist as firms camouflage their smuggling activities by also conducting legal trade.

Another strand of the theoretical literature, initiated by Pitt (1981), analyzes the determinants of trade misinvoicing. Pitt argues that smuggling is positively correlated with the price disparity, defined as the difference between the actual domestic price and the tariff-inclusive world market price. If, for example, the domestic price of an exportable good exceeds its world market price, it can only be exported legally at a loss, indicating that most of the actual exports are traded illegally. Martin and Panagariya (1984) and Norton (1988) consider the costs of smuggling. They find that stricter law enforcement serves as a deterrent to smuggling. Pitt (1984) analyzes the black market premium (BMP) for foreign exchange as a determinant of smuggling. He finds that the black market equilibrates the supply of foreign exchange from illegal exports and its demand to purchase illegal imports. Biswas and Marjit (2007) find that export (import) underinvoicing is positively (negatively) correlated with the BMP, since the foreign exchange from the unreported transaction is sold (paid) on the black market.

The empirical literature studies the determinants of trade misinvoicing using data on trade discrepancy. These studies conclude that if the import figures of the importing country fall short of (exceed) the export figures of the corresponding exporting country, import underinvoicing (overinvoicing) must be taking place in the importing country.2 As the empirical literature is vast, Table 1 provides a comprehensive overview and summarizes the findings of previous studies.

Bhagwati (1964) analyzes trade data for Turkey and its major trading partners. He finds import underinvoicing for transport equipment and machinery. Both product categories feature high tariffs that by far exceed the BMP and thus motivate import underinvoicing. McDonald (1985) finds that export underinvoicing is positively correlated with export taxes and BMP. Pohit and Taneja (2003) conclude that informal trade between India and Bangladesh results in avoidance of administrative burden. Fisman and Wei (2007) find that misinvoicing for cultural properties is highly correlated with the extent of corruption in the exporting country. Berger and Nitsch (2008) confirm this finding for an extended set of product categories. Beja (2008) estimates the amount of China's unreported trade between 2000 and 2005 to be $1.4 trillion. Farzanegan (2008) estimates export and import misinvoicing in Iran using a MIMIC approach and finds that the smuggling of legal goods in Iran accounted for 6-25% of total trade between 1970 and 2002.

3. Micro-Foundations of Smuggling Incentives

We argue that smugglers of illegal goods respond to different incentives than do smugglers of legal goods. The following uses a simple microeconomic approach to determine the expected impact of different determinants on both types of smuggling.3

Determinants of Illegal Goods Smuggling

The representative risk-neutral Mexican smuggler maximizes her expected profit with respect to the amount of illegal goods or persons to be smuggled into the United States, [S.sup.ill]. Equation 1 outlines the revenue from smuggling illegal goods, R([S.sup.ill]):

R ([S.sup.ill] = (1 + v)e[p.sup.US] [S.sup.ill]. (1)

The smuggler sells Sm illegal Mexican goods at price [p.sup.US] in the United States and converts the dollar-denominated proceeds on the black market to Mexican pesos, earning BMP v over the official exchange rate e.4 The expected costs of smuggling, E[C([S.sup.ill])], arise from the risk of being caught by U.S. Border and Customs Protection,5 as outlined in Equation 2:

E[C([S.sup.ill])] = prob([S.sup.ill], H)F,

with

[partial derivative]prob([S.sup.ill],H)/[partial derivative][S.sup.ill] > 0, [[partial derivative].sup.2]prob] [([S.sup.ill]).sup.2] > 0, [partial derivative]prob([S.sup.ill],H)/[partial derivative]H > 0. (2)

The smuggler is apprehended with probability prob([S.sup.ill], H) and faces the punishment cost F. We assume that the probability of apprehension is a convex function of the amount of illegal goods being smuggled and depends positively on the exogenous border enforcement, H; that is, the more officers patrolling the U.S.-Mexico border, the more likely smugglers are to be caught. If the smuggler is apprehended, she will be sentenced to prison. The cost of punishment F therefore represents the opportunity cost of lost labor income, (1 - u)w, during imprisonment. The higher the Mexican wages, w, and the lower the Mexican unemployment rate, u, the higher the cost of punishment, F:

F = f[(1 - uw], with [partial derivative]f[(1 - u)w]/[partial derivative]u < 0, [partial derivative]f[(1 - u)w]/[partial derivative]w > 0. (3)

Using Equations 1-3, the expected nominal profit from smuggling illegal goods E([[pi].sup.ill]) is

E ([[pi].sup.ill]) = (1 + v)[ep.sup.US] [s.sup.ill ] - prob ([S.sup.ill,] H)f[(1 - u)w]. (4.1)

To study the determinants of smuggling illegal goods in real terms, we denominate the expected profit in Mexican goods by dividing Equation 4.1 by the Mexican price index, [p.sup.MEX]. Equation 4.2 shows the expected real profit from smuggling, whereby the real exchange rate is defined as e = [ep.sup.US]/[p.sup.MEX]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII](4.2)

Real profit optimization with respect to the amount of smuggling, [S.sup.ill], yields the result that the marginal revenue from smuggling equals the marginal cost of smuggling:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Equation 5 determines how the optimal amount of illegal goods to smuggle, [S.sup.ill], reacts to changes in the incentive variables. We derive the following hypotheses: A higher BMP, v, increases the incentive to smuggle, d[S.sup.ill]/dv > 0, ceteris paribus, as converting dollars into pesos on the black market is more profitable. A higher real exchange rate, that is, a real depreciation of the peso against the dollar, increases smuggling, d[S.sup.ill]/d[epsilon] > 0, ceteris paribus, as revenues rise in terms of Mexican goods. (6) Higher Mexican wages and lower Mexican unemployment reduce the incentive to smuggle, that is, both d[S.sup.ill]/dw < 0 and d[S.sup.ill]/du > 0 hold. Hence, better Mexican job prospects decrease smuggling by raising the opportunity costs of imprisonment if apprehended, (1 - u)w. Thus, we expect smuggling activities to rise during Mexican recessions, when Mexican labor market conditions worsen. More intense border enforcement should lead to a decrease in the smuggling of illegal goods, d[S.sup.ill]/dH < 0, ceteris paribus, as this increases the probability of apprehension and, thus, the expected cost of smuggling.

Determinants of Legal Goods Smuggling/Trade Misinvoicing

Export Misinvoicing

A Mexican entrepreneur exports a given amount of legal goods, X, to the United States. In order to save on Mexican income taxes and to benefit from the BMP, she has an incentive not to report the total amount of exports. Export underinvoicing, [S.sup.x] > 0, thus means that the reported amount of exports, X - [S.sup.x], is lower than the actual amount of exports, X. (7) Equation 6 describes the Mexican exporter's expected profits, E([[pi].sup.x]):

E([pi].sup.x]) = (1 - t)[ep.sup.US](x- [S.sup.x]) + (1 + v)[ep.sup.US][S.sup.x] - prob([S.sup.X)]F, (6)

where

[partial derivative] prob([S.sup.x])/[partial derivative][S.sup.x]>O and [[partial derivative].sup.2] prob([S.sup.x])/[([partial derivative][S.eup.x]).sup.2] > 0.

Given the total amount of exports, X, the Mexican exporter decides how many exports to report and how many to underinvoice. She sells the reported (legal) exports X - [S.sup.x] at [p.sup.US] in the United States and converts the dollar-denominated proceeds at the official exchange rate e into pesos, generating a legal after-tax export revenue of (1 - t)[ep.sup.US](x - [S.sup.x]), where t denotes the income/profit tax. (8) The unreported (misinvoiced) exports, [S.sup.x], are sold at [p.sup.US] in the United States. The dollar-denominated smuggling revenue is then converted into pesos on the black market, where the misinvoicer profits from the BMP, v, over the official exchange rate, e.

The expected cost of export underinvoicing arises from the risk that the misinvoicing will be detected by the authorities with probability prob([S.sup.x]) and that the exporter will subsequently face the punishment cost F, which represents exogenous expenses for bribes or fines. The detection probability is assumed to be convex in the amount of export underinvoicing. Dividing Equation 6 by the Mexican price index, [p.sup.MEX], and using the definition of the real exchange rate, [epsilon] = [ep.sup.US]/[P.sup.MEX], yields the Mexican export underinvoicer's real expected profit:

E([[pi].sup.x]/[p.sup.MEX]) = (1 - t)[epsilon]X + (v + t)[epsilon][S.sup.x] - prob]([S.sup.x]) F/[p.sup.MEX].

Real profit optimization over the amount of export underinvoicing, [S.sup.x], again yields the result

that the marginal revenue equals the marginal cost of smuggling:

(v + t)[epsilon] = [partial derivative]prob([S.sup.x])/[partial derivative][S.sup.x] F/[p.sup.MEX; with [[partial derivative].sup.2] prob([S.sup.x])/[([partial derivative][S.sup.2]) > 0.(8)

We hypothesize the following effects of smuggling incentives on export underinvoicing: A higher BMP, v, should cause export underinvoicing to rise ceteris paribus, d[S.sup.x]/dv > 0, as the exchange rat--adjusted price spread between unreported and reported exports increases. A real depreciation of the peso against the dollar should lead to higher export underinvoicing ceteris paribus, d[S.sup.x]/d[epsilon] > 0, as Mexican goods become more competitive. (9) Higher Mexican incomel profit taxes, t, should lead to more export underinvoicing ceteris paribus, d[S.sup.x]/dt > 0, as illegal/ unreported Mexican exports are not subject to taxation and thus become more competitive over legal/reported Mexican exports. Tax evasion therefore appears to be an important motive for export misinvoicing.

Import Misinvoicing

The Mexican entrepreneur imports a fixed amount of legal goods, M, from the United States and decides how many imports to report, M - [S.sup.M], and how many to underinvoice, [S.sup.M] > 0. Equation 9.1 describes the Mexican importer's expected profit, E([[pi].sup.M]):

E([[pi].sup.M])=(1 - t)[R(M)-[ep.sup.US](1 + q)(M -[S.sup.M])] -(l + v)[ep.sup.US][S.sup.M] - prob([S.sup.M])F, (9.1)

where

[partial derivative]prob([S.sup.M])/[partial derivative][S.sup.M] > 0 and [[partial derivatie].sup.2] prob([s.sup.M])/[([partial derivative][S.sup.M]).sup.2] > 0.

The Mexican entrepreneur imports M goods--some reported, some unreported--from the United States and sells them in Mexico, earning R(M) pesos. She spends [ep.sup.US](1 + q)(M - [S.sup.M]) pesos to import the reported (legal) American goods, where q denotes the Mexican import tariff levied on reported American goods. After paying the Mexican income/profit tax, t, the Mexican importer makes an after-tax profit of (1 - t)[R(M) - [ep.sup.US](1 + q)(M - [S.sup.M])] pesos on her reported transactions. For the unreported (misinvoiced) U.S. imports, [S.sup.M], she spends (1 + v)[ep.sup.US][S.sup.M] pesos paying the BMP, v, to buy the required dollars on the black market. The import misinvoicer faces the expected cost of punishment prob([S.sup.M])F, where prob([S.sup.M]) denotes the probability of being caught and F denotes the subsequent bribes or fines. Equation 9.2 describes the Mexican importer's real expected profit:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9.2)

Real profit optimization with respect to the amount of import underinvoicing, [S.sup.M], yields the result that the marginal benefit equals the marginal cost of smuggling: (10)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

Intuitionally, the optimal amount of import underinvoicing [S.sup.M] reacts to changes in incentive in the opposite direction of the optimal amount of export underinvoicing, thus:

A higher BMP, v, decreases the incentive to underinvoice imports ceteris paribus, d[S.sup.M]/dv < O, as it becomes more expensive to buy U.S. dollars for unreported imports on the black market.

A real depreciation of the peso against the dollar, d[epsilon] > 0, should decrease the amount of import underinvoicing ceteris paribus, d[S.sup.M]/d[epsilon] < 0, as Mexican products gain competitiveness over misinvoiced American products.

A rise in Mexican incomelprofit taxes should reduce import underinvoicing ceteris paribus, d[S.sup.M]/dt < 0, as illegal/unreported Mexican imports cannot be claimed as tax exempt and, thus, lose profitability compared to legal/reported Mexican imports.

Finally, we expect higher tariff rates to increase import underinvoicing, ceteris paribus, d[S.sup.M]/dq > 0, as tariff evasion increases the profitability of unreported imports.

4. Empirical Methodology

The MIMIC model relates observable causal and indicator variables to a per se unobservable phenomenon. (11) Thus, it allows us to deal with the multiple causes and the multiple effects of smuggling across the U.S.-Mexico border. The MIMIC model has two parts: the structural equation model and the measurement model. 12 In the structural equation model, smuggling is determined by a set of exogenous causes, in our case the microeconomic smuggling incentives described above. The structural equation model is given by

[eta] = [gamma]' + [??], (11)

where each [x.sub.i], i = 1, ..., q in the (q x 1) vector x is a potential cause of the latent variable rl and [gamma]' = ([[gamma].sub.i], [[gamma].sub.2], ..., [[gamma].sub.q]) is a vector of coefficients describing the relationships between the latent variable and its causes. The error term g represents the component of the latent variable [eta] not explained by the causes. The variance of g is denoted by [psi]. The measurement model links the latent variable to its indicators:

y = [lambda][eta][ + [ [[epsilon]. (12)

In this model, y' = ([y.sub.1], [y.sub.2], ..., [y.sub.p]) is a vector of indicator variables that measures the latent variable smuggling (see section 5). [lambda] is the vector of regression coefficients, and [epsilon]' is a (1 x p) vector of white noise disturbances, that is, [epsilon] ~ (0, [[THETA].sub.[epsilon]]).

The structural and the measurement model equations can be used to derive a reducedform multivariate regression model:

y = [product] x + z, (13)

where [product] = [[lambda].sub.[gamma]' is a matrix with rank equal to 1. The endogenous variables [y.sub.j], j = 1, ..., p are the latent variable [eta]'s indicators, and the exogenous variables [x.sub.i], i = 1, ..., q are its causes. The error term z = [lambda][zeta] + [epsilon] is a (p x 1) vector of linear combinations of the white noise error terms [??] and [epsilon] from the structural equation and the measurement model, that is, z - (0, [OMEGA]). The covariance matrix [OMEGA] is given by Cov(z) = E[[[lambda].sub.[??]] + [epsilon])] = [lambda][lambda]' [psi] + [[THETA].sub.[epsilon] and is constrained like If. The estimation of the model therefore requires the normalization of one of the elements of the vector X to an a priori value (Bollen 1989).

The model's parameters are estimated using the variances and covariances among the observable causal and indicator variables. Assuming that an unobservable variable generates this pattern, the decomposition of the MIMIC model's covariance matrix yields the structure between the observed variables and the latent variable (see Bollen [1989] for details). The values for the parameters and covariances are then estimated to produce a MIMIC model covariance matrix that is as close as possible to the sample covariance matrix of the observed causes and indicators.

5. Measurement of Smuggling

In the measurement model, the indicators are regressed on a--per se undefined--latent variable. After defining each type of smuggling, we select indicators to measure each type appropriately. Thus, the meaning of the latent variable depends on how well the indicators correspond to the operational definition.

Of course, indicators are often only imperfectly linked to the latent variable (Bollen 1989), but it is obvious from Equation 12 that all of them are alternative measures of the same latent variable: That is, a change in the latent variable affects its indicators. This can be clarified further by taking the structural model into account. Within the theoretical framework from section 3, we identify the microeconomic incentives that determine the profitability of each type of smuggling. If, for example, border enforcement is intensified, the cost for smugglers of illegal goods increases, and the latent macroeconomic amount of illegal goods smuggled should decrease. Thus, a change in the microeconomic incentive structure transmits uniformly to the macroeconomic aggregate of all types of smugglers of illegal goods be it smugglers of illegal drugs or illegal immigrants. The indicators discussed below all measure the total amount of each type of smuggling, as determined by the microeconomic incentive structure.

Indicators for Smuggling of Illegal Goods

Our conceptual definition of illegal goods smuggling comprises the inflow of illegal drugs and illegal immigrants from Mexico to the United States. We do not consider smuggling in other types of illegal goods, for example, alcohol or bootlegs. The reasons for this are that illegal drugs and immigrants are at the center of the political debate on whether to increase U.S. border patrol and estimates about the size of these types of smuggling necessary to calculate the time trend--are available.

To explain illegal goods smuggling in the measurement model, in particular illegal drugs and immigrants, we use the following macroeconomic indicators: linewatch and non-linewatch apprehensions, real drug seizures, and availability of drugs in the United States. Smugglers of illegal drugs and illegal immigrants have in common that they have to cross the U.S.-Mexico border to bring their illegal "freight" to the United States. To stop this illegal inflow, the U.S. border patrol makes an enormous effort to apprehend smugglers crossing the border. One of the objectives of the National Border Patrol Strategy of 2004 (Office of Border Patrol 2004) is to "detect, apprehend, and deter smugglers of humans, drugs, and other contraband." If illegal goods smuggling increases the number of apprehensions should also increase, ceteris paribus. Thus, we expect that linewatch and non-linewatch apprehensions, that is, the number of persons apprehended at the U.S.-Mexico border and inside the United States, are positively correlated with the smuggling of illegal goods.

Another indicator of illegal goods smuggling is drugs seized by the border control. Given the efforts of the United States to fortify the border against the inflow of illegal goods, we expect drug seizures to increase as illegal goods smuggling rises, ceteris paribus. Of course, several smugglers successfully cross the border and succeed in their smuggling activities. Thus, we also include the availability of drugs as another indicator in order to account for illegal goods that have been smuggled into the United States successfully (that is, undetected). We expect drug availability to increase as illegal goods smuggling rises, ceteris paribus.

Indicators for Smuggling of Legal Goods

In contrast to smugglers of illegal goods, smugglers of legal goods break the law from their offices rather than at the border. As no data on convicted misinvoicers are available, we employ balance of payments data--in particular trade discrepancies and data on errors and omissions--to proxy legal goods smuggling as common in the literature. Assuming that industrialized countries like the United States correctly report trade figures, discrepancies between U.S. figures and Mexican figures result from misreporting by Mexican importers/ exporters. Export underinvoicing by Mexican exporters is the difference between U.S. imports from Mexico (reported by the United States) and Mexican exports to the United States (reported by Mexico).13 Import underinvoicing by Mexican importers is the difference between U.S. exports to Mexico (reported by the United States) and Mexican imports from the United States (reported by Mexico).

Data on errors and omissions are included in the Mexican balance of payments and are used as a second indicator of legal goods smuggling.14 Unreported Mexican exports (export underinvoicing) lead to inflows of foreign exchange. These exports do not appear in the trade balance but rather increase the errors and omissions of the Mexican balance of payments by the amount of export underinvoicing. We therefore conclude that the higher the export underinvoicing, the higher the errors and omissions, ceteris paribus. Likewise, the lower the import underinvoicing, the higher the errors and omissions.

[FIGURE 1 OMITTED]

6. Empirical Analysis

This section presents the results of our MIMIC model estimations and the long-term trends in the smuggling of illegal goods and legal goods (export and import misinvoicing) across the U.S.-Mexico border. Recognizing these different types of smuggling as outlined in section 3, we estimate three different MIMIC models.

The first model tests whether the microeconomic causal variables affect the smuggling of illegal goods, as hypothesized in section 3. Figure 1 illustrates the path diagram of illegal goods smuggling using the indicators explained in section 5. Table A1 in the Appendix presents the empirical identification, data sources, and definitions of the theoretical variables.

The second and third models test the determinants of legal goods smuggling, also hypothesized in section 3 using the indicators outlined in section 5. Figure Al in the Appendix displays the path diagrams for export and import misinvoicing.

Data

To estimate the MIMIC models, we use monthly data from 1975 to 2004. Because data on the BMP are available only through December 1998 (the date of the last issue of Pick's World Currency Report) and data on errors and omissions in the Mexican balance of payments are available only from January 1980, however, some of our estimations are limited to the 1980-1998 time period.

We test for unit roots, as MIMIC models with nonstationary time series produce misleading estimates. We therefore examine each time series for those periods subsequently used in the estimations under the null hypothesis of a unit root against the alternative of stationarity using the Augmented Dickey Fuller (ADF) test. The Kwiatkowski, Phillips, Schmidt, and Shin test, which tests stationarity against the alternative of the presence of a unit root, is used to cross-check the ADF test's results.

We find that most variables, except for the BMP and the real exchange rate from 1975-1998 and 1975-2004, are not stationary in levels. However, for 1980-1998 and 1980-2004, we cannot reject the null hypothesis of a unit root for the BMP, as both unit root tests produce divergent results. Consequently, we use the BMP in first differences in our estimations covering these time periods. Other variables found nonstationary in levels are also transformed in this way and re-tested. As the null hypothesis of a unit root is now rejected, we use the first difference of all variables except for the BMP and real exchange rate from 1975-1998 and 19752004 in the MIMIC model estimations. (15)

Estimation Results

Tables 2 and 3 present the results of our MIMIC model estimations for smuggling illegal and legal goods. (16) As explained in section 4, the estimation of a MIMIC model requires the normalization of one indicator for each latent variable that also determines the unit of measurement of the latent variable (Bollen 1989). (17) In the illegal goods smuggling estimations, we set the coefficient of linewatch apprehensions to 1. In the case of legal goods smuggling, we set the variable errors and omissions to 1 for export misinvoicing and to -1 for import misinvoicing. (18)

For the smuggling of illegal goods, we estimate seven different MIMIC model specifications by varying either the time period or the set of indicator variables. We include all causal variables considered in section 3 except for the BMP, which is not included in estimations for 1999-2004. (19) In the four model specifications for the smuggling of legal goods, we vary the time period only.

The MIMIC model estimations for the smuggling of illegal goods show that this kind of smuggling reacts only to changes in smuggling costs. Thus, the unemployment rate, real wages, and border enforcement are the major causes and have the theoretically expected impact on smuggling. Higher wages and lower unemployment increase opportunity costs during imprisonment and, thus, reduce smuggling in illegal goods. More intense border enforcement significantly deters illegal goods smuggling for all specifications estimated. This variable approximates the probability of being caught smuggling at the border. The higher this probability, the higher the expected costs for smugglers and, thus, the lower the smuggling of illegal goods, ceteris paribus. By contrast, changes in the variables affecting revenues from smuggling illegal goods do not significantly influence smuggling: That is, the BMP and the real exchange rate are not significant for any specification. It seems that smugglers live at the subsistence level and have to smuggle illegal goods to earn a living for their families. The decision whether or not to engage in smuggling is then based on the opportunity cost, that is, on the employment opportunities in the official economy and on the probability of being apprehended.

Turning to the indicators, we find a strongly significant, positive relationship between illegal goods smuggling and the number of apprehensions, which confirms our hypothesis that the number of failed smuggling attempts indicates the level of illegal goods smuggling. The relationship between drug seizures/drug availability and smuggling is only sometimes statistically significant. While we find the hypothesized positive sign for all specifications, drug seizures are significant for specifications 1 and 3 only while drug availability is not significant.

In the MIMIC models for the smuggling of legal goods, all causal variables except for the BMP are statistically significant at conventional significance levels and have the expected sign. Hence, the data confirm the theoretical hypotheses in section 3. A real depreciation of the peso against the U.S. dollar leads to higher export underinvoicing as the competitiveness of Mexican goods increases. Moreover, the higher Mexican income/profit taxes are, the stronger the incentive is to underinvoice exports, as illegal/unreported Mexican exports are not taxed and ate thus more competitive. Again, an important motive to underinvoice exports is tax evasion. In the case of import misinvoicing, real peso depreciation against the U.S. dollar decreases the amount of import underinvoicing as Mexican products gain competitiveness over misinvoiced U.S. imports. A rise in Mexican income/profit taxes lowers import underinvoicing. Illegal/ unreported Mexican imports cannot be claimed as tax exempt and thus lose profitability compared to legal/reported Mexican imports, which confirms our tax evasion argument. In contrast, a higher tariff rate increases import underinvoicing, supporting the common view that import underinvoicing is motivated by tariff evasion.

All estimated MIMIC models show satisfactory goodness-of-fit statistics, as shown in Tables 2 and 3. The models fit the data fairly well, and the q-plots demonstrate a sufficiently normal distribution of the standardized residuals, that is, of the difference between the observed and the fitted covariance matrix. Thus, we can accept the validity of the estimated models and conclude that all specifications are suitable to calculate long-term trends in the smuggling of illegal and legal goods.

Long-Term Trends in Illegal Goods Smuggling

The estimated MIMIC coefficients allow us to determine the dimensionless time pattern of smuggling only. To obtain the market value of smuggling over time, we convert the MIMIC index into "real-world" figures measured in U.S. dollars. In the first step, we calculate an exogenous base value for illegal goods smuggling across the U.S.-Mexico border in 2000 using expert estimates. As mentioned in section 5, we focus on the two types of smuggled illegal "goods" prominently discussed in the media: illegal immigrants and illegal drugs. In the second step, this base value is used to calibrate a time series of smuggling by applying the benchmarking procedure promoted by Dell'Anno and Schneider (2006), Dell'Anno (2007), and Dell'Anno and Solomon (2008).

The average inflow of illegal (unauthorized) adult Mexican immigrants to the United States is estimated at about 330,000 per year between 2000 and 2007 (Hoefer, Rytina, and Baker 2008; Passel and Cohn 2008). Because we cannot assess the "market value" of these illegal immigrants, we calculate the average wage earned while working in the United States illegally using the Mexican Migration Project (MMP) database. Since 1982, the MMP has conducted annual surveys of (illegal) Mexican immigrants. Using data on the employment characteristics of Mexicans who entered the United States illegally, including data on their duration of stay, we calculate the average salary an illegal Mexican immigrant earns during her stay in the United States. Table 4 illustrates that illegal Mexican immigrants, on average, worked in the United States for 20.08 months and earned $26,325. Based on this, we calculate that the 330,000 illegal Mexican immigrants earn wages amounting to $8.7 billion each year.

To calculate the base value of illegal drugs smuggled across the U.S.-Mexico border, we employ expert estimates, as illustrated in Table 5. According to Rhodes et al. (2001), Americans spent $61.2 billion on illegal drugs in 2000. Using the estimated "Mexican" share of these drugs, (20) we quantify the market value of drugs smuggled across the U.S.-Mexico border at $31.4 billion in 2000. Aggregating the calculated size of illegal immigration and illegal drugs smuggling, we obtain an exogenous estimate for illegal goods smuggling across the U.S.-Mexico border of $40.1 billion in 2000.

This base value allows us to calculate a time series for illegal goods smuggling by applying a benchmarking procedure. Unfortunately, no consensus exists in the literature with regard to which benchmarking procedure to use. We use the methodology promoted by Dell'Anno and Schneider (2006), Dell'Anno (2007), and Dell'Anno and Solomon (2008). In the first step, the MIMIC model index of smuggling is calculated by multiplying the coefficients of the significant causal variables by the respective raw time series. For the numerical example of specification 4 the structural equation is given as (21)

[[??].sub.t]/[Smugglers.sub.2000] = 0.05 x [x.sub.1t] - 0.05 x [x.sub.2t] - 0.64 x [x.sub.3t] (14)

and measures illegal goods smuggling per apprehended smuggler in 2000 according to the MIMIC model's identification rule. (22) Next, this index is converted into a time series of illegal goods smuggling, which takes up the base value of $40.1 billion in 2000. Thus, the annual U.S. dollar amount of illegal goods smuggling tit at time t is given as follows:

[[??].sub.t]/[Smugglers.sub.2000] [Smugglers.sub.2000]/[[??].sub.2000] [[eta].sup.*.sub.2000] = [[??].sub.t]/ [[??].sub.t] [[??].sup.*.sub.2000] = [[??].sub.t], (15)

where ([[??].sub.t]/[Smugglers.sub.2000]) denotes the value of the MIMIC index at t according to Equation 14, ([[??].sub.2000]/[Smugglers.sub.2000]) is the base value of this index in 2000, and [[eta].sup.*.sub.2000] is the exogenous estimate of illegal goods smuggling, amounting to $40.1 billion in 2000.

[FIGURE 2 OMITTED]

The final estimates of illegal goods smuggling over the last three decades are calculated using specifications 4 through 7. (23) As shown in Figure 2, all calculated indices have a similar pattern. (24) Table A2 in the Appendix presents selected annual estimates for illegal goods smuggling.

Illegal goods smuggling seems to be driven largely by macroeconomic conditions in Mexico and by changes in U.S. border enforcement policy. The two major Mexican recessions, triggered by a debt crisis in 1982-1983 and by a currency crisis in 1994-1995, resulted in a significant increase in the smuggling of illegal goods to $113 billion in 1983 and $87 billion in 1995. Both economic downturns were associated with rising unemployment and falling real wages in Mexico and were a push factor for Mexican smugglers. As Mexican labor market conditions worsened, many Mexicans chose to engage in illegal smuggling activities as an alternative source of income.

We also find evidence that a stricter U.S. border enforcement policy since the Immigration Reform and Control Act of 1986 may have contributed to a long-term decline in the smuggling of illegal goods, which fell from $116 billion in 1986 to $27 billion in 2004. The number of person-hours spent by U.S. border patrol policing the U.S.-Mexico border increased from 2.7 million in 1986 to 9.7 million in 2004. This rise in border enforcement activities effectively raised the probability of apprehension, thereby reducing smuggling. In 2003, the pattern of illegal goods smuggling reversed as an unintended consequence of a change in U.S. drug policy (Carpenter 2005). U.S. officials believed that by focusing on the drug cartels' top figures, rather than on petty smugglers at the border, they could achieve huge decreases in drug trafficking. But the new policy led only to a decentralization of the drug trade: Instead of the kingpins who had controlled it before, there are now more than 300 small groups engaged in illegal drug smuggling (Carpenter 2005).

[FIGURE 3 OMITTED]

Long-Term Trends in Legal Goods Smuggling

As with illegal goods smuggling, Equation 15 is applied to convert the MIMIC index into a time series of legal goods smuggling using the significant causal variables in specifications 9 (export misinvoicing) and 11 (import misinvoicing). The base values for benchmarking are taken from Eggerstedt, Hall, and van Wijnbergen (1995), who present estimates for misinvoicing in the U.S.-Mexican trade using U.S. Department of Commerce and Banco de Mexico data. We use the overinvoicing estimate of $588.3 million in 1984 as the base value for export misinvoicing and the underinvoicing value of $914.4 million in 1984 for import misinvoicing.

Figure 3 shows the estimated time series for legal goods smuggling. While export misinvoicing exhibits temporary fluctuations but no time trend, import misinvoicing is permanently affected by U.S.-Mexican trade integration. The reduction of Mexican tariffs on U.S. imports after Mexico's accession to GATT in 1987 and to NAFTA in 1994 resulted in a permanent switch from import underinvoicing--motivated by tariff evasion--to import overinvoicing--motivated by tax evasion.

7. Summary and Conclusion

This article examines the determinants of and long-term trends in smuggling across the U.S.-Mexico border, distinguishing between the smuggling of illegal and legal goods. Working out the microeconomic incentives of the two types of smuggling, we hope to improve understanding of this phenomenon. It seems reasonable to assume that smugglers who traffic illegal drugs or illegal immigrants respond to different incentives than do trade misinvoicers. As smuggling is an illegal and, thus, unobservable, activity, we use a MIMIC approach in our analysis and calculate the long-term trends in illegal and legal goods smuggling across the U.S.-Mexico border.

The results of the MIMIC model are robust and confirm most of our theoretical hypotheses. We find that illegal goods smuggling declines when Mexican labor market conditions improve or when U.S. border enforcement activities are intensified, as the cost of smuggling rises in this context. Confirming the competitiveness argument, export (import) misinvoicing is positively (negatively) correlated with real peso depreciation. Import misinvoicing is positively correlated with Mexican import tariffs, pointing to the incentive of tariff evasion. Export (import) misinvoicing is positively (negatively) correlated with Mexican taxes on income and profit, pointing to the incentive of tax evasion.

The estimated long-term trends for both types of smuggling show the sensitivity of smuggling to major macroeconomic events. Import misinvoicing has switched from underinvoicing to overinvoicing over the last 20 years as a result of reduced import tariffs, following Mexico's accession to GATT in 1987 and to NAFTA in 1994. Illegal goods smuggling rose temporarily during the Mexican recessions in 1982-1983 and 1995, but the overall trend is negative, decreasing by almost $90 billion from 1984 to 2004; this decline can be attributed to improved labor market conditions in Mexico and a successful U.S. border enforcement policy. Indeed, the increase in U.S. border patrol hours has increased the probability of apprehension and strengthened the deterrent to smuggle.

Analyzing smuggling using a MIMIC model has some shortcomings that are, however, widely accepted in other fields that involve the study of unobservable phenomena, such as the shadow economy or corruption. First, although the model tracks the development of smuggling over time, the estimations for the volume of smuggling depend on the exogenous estimate used for calibration. Researchers can carefully check its size and reliability, but the final estimate remains an approximation. Second, difficulties arise for MIMIC applications to time-series data because of the limitations in the ability to check the residuals' properties. Finally, other variables for which data are not available, such as tax morality or socioeconomic factors, may influence smuggling.

Nevertheless, this article contributes to the understanding of smuggling, and the results have important implications for the policy debate. The smuggling of illegal drugs and immigrants across the U.S.-Mexico border remains a major issue for U.S. national security. Illegal drug abuse leads to casualties, rising health care costs, and lower employment in the United States (French, Roebuck, and Alexandre 2001). In addition, illegal immigration not only affects labor market conditions in the United States but represents a serious humanitarian crisis. It is unbearable that myriad Mexicans die when attempting to cross the border illegally. (25)

Despite the successful border enforcement policy, several options are available to further reduce illegal goods smuggling. Increased bilateral trade and U.S. aid and foreign direct investment to Mexico, for example, would improve Mexican labor market conditions, thereby reducing the incentive to smuggle. The United States could also further increase linewatch hours or invest in border patrol technologies. Finally, the United States could provide financial and/or technical support to intensify patrolling activities on the Mexican side of the border.

Trade misinvoicing seems to be a less serious problem, given that it is a relatively small-scale financial crime with no loss of human life. Also, the scope for political intervention is limited. Tariffs have already been reduced significantly, and it is unlikely that exchange rate policy would be used to combat trade misinvoicing.

Appendix

[FIGURE A1 OMITTED]

Table Al. Data Sources and Definitions

Variable Definition

BMP (black (Black market exchange rate--official
 market premium) exchange rate)/official exchange rate
Real exchange rate Nominal official exchange rate
 (peso/$U.S.) x U.S.
 Consumer Price Index (CPI)/Mexican
 (MX) CPI
MX unemployment Unemployed persons as % of total labor
 rate force, seasonally adjusted
MX real wages Nominal wage in manufacturing deflated
 with MX CPI, seasonally adjusted
U.S. border enforcement Number of person-hours spent
 by the U.S. Customs and
 Border Protection (CBP) for border
 patrols/total apprehensions, seasonally
 adjusted
U.S. linewatch Individuals apprehended by the
 apprehensions CBP at international
 boundaries of the United
 States, seasonally adjusted
U.S. non-linewatch Individuals apprehended by the CBP
 apprehensions inside the United States
 at traffic checkpoints, raids on
 businesses, or interior patrols,
 seasonally adjusted
U.S. real drug seizures Illegal drugs seized by the CBP,
 in million $U.S., deflated by
 U.S. CPI
U.S. drug availability % of U.S. 12th-graders
 reporting that "marijuana is
 fairly or very easy" to obtain
MX taxes on % of GDP
 income/profit
MX taxes on % of imports
 international trade
MX errors and Balance of payments position,
 omissions million $U.S.
Import misinvoicing [U.S. exports--MX imports
 (CIF, FOB adjusted)]

Export misinvoicing [U.S. imports (CIF, FOB
 adjusted)--MX exports]

Variable Source

BMP (black 1975-1982: Pick (1955-1982),
 market premium) various issues; 1983-1998:
 Pick (1983-1998), various issues
Real exchange rate Nominal exchange rate:
 International Monetary Fund
 (IMF) International Financial Statistics;
 MX CPI: Banco de
 Mexico; U.S. CPI: Bureau of
 Labor Statistics
MX unemployment 1975-1984: Fleck and Sorrentino
 rate (1994); 1985-2004: DECD Main
 Economic Indicators
MX real wages 1975M1-1998M5: Hanson and
 Spilimbergo (1999),
 1998M6-2004M4: Instituto
 National de Estadfstica,
 Geografia e Informatica (INEGI)
U.S. border enforcement Unpublished records of the U.S.
 Immigration and
 Naturalization Service (INS),
 Hanson (2006)
U.S. linewatch Unpublished records of the INS, Hanson
 apprehensions (2006)
U.S. non-linewatch Unpublished records of the INS, Hanson
 apprehensions (2006)
U.S. real drug seizures Department of Homeland Security, Hanson
 (2006)
U.S. drug availability Johnston et al. (2007)
MX taxes on 1975-2000 IMF Government
 income/profit Statistics, 2001-2004 OECD
 Revenue Statistics.
MX taxes on 1975-2000 IMF Government
 international trade Statistics, 2001-2004 OECD
 Revenue Statistics.
MX errors and IMF, International Financial
 omissions Statistics
Import misinvoicing 1975-1980: IMF Directions of
 Trade Statistics (DOTS)
 Historical, 1981-2004: IMF DOTS
Export misinvoicing 1975-1980: IMF DOTS Historical, 1981-2004:
 IMF DOTS

Table A2. Estimates for Illegal and Legal Goods Smuggling

Year Illegal Goods Export Import
 Smuggling Misinvoicing Misinvoicing
 (billion $U.S.) (billion $U.S.) (a) (billion $U.S.) (a)

1976 75.52
1977 84.68
1978 84.16
1979 78.81
1980 69.45 -0.03 0.l9
1981 71.99 -0.18 0.00
1982 74.24 -0.51 0.73
1983 113.11 -0.69 1.66
1984 115.99 -0.59 0.91
1985 114.36 -0.66 1.03
1986 116.36 -0.36 -0.59
1987 81.69 -0.47 -0.31
1988 86.58 -0.36 -0.71
1989 68.11 -0.19 -0.93
1990 76.20 -0.23 -0.18
1991 77.28 -0.29 0.52
1992 79.42 0.00 -1.17
1993 73.16 0.22 -3.30
1994 62.32 0.06 -3.50
1995 97.23 -0.51 -0.83
1996 79.77 -0.61 -0.32
1997 62.12 -0.36 -1.66
1998 50.07 -0.18 -2.59
1999 39.92 -0.02 -3.36
2000 40.10 -0.08 -3.03
2001 29.61 0.04 -3.77
2002 22.86 0.03 -3.83
2003 23.43 -0.06 -3.47
2004 27.36 -0.30 -2.28

The indices for illegal goods smuggling, export misinvoicing, and
import misinvoicing are calculated using specifications 4, 9, and
11, respectively.

(a) Positive values indicate underinvoicing; negative values
indicate overinvoicing.

References

Beja, Edsel L. 2008. Estimating trade mis-invoicing from China: 2000-2005. China & Worm Economy 16:82-92.

Berger, Helge, and Volker Nitsch. 2008. Gotcha! A profile of smuggling in international trade. CESifo Working Paper No. 2475.

Bhagwati, Jagdish N. 1964. On the under-invoicing of imports. Bulletin of the Oxford University, Institute of Economics and Statistics 26:389-97.

Bhagwati, Jagdish N., and Bent Hansen. 1973. A theoretical analysis of smuggling. The Quarterly Journal of Economies 87:172-87.

Biswas, Amit K., and Sugata Marjit. 2007. Preferential trade and mis-invoicing: Some analytical implications. International Review of Economies & Finance 16:13-8.

Bollen, Kenneth A. 1989. Structural equations with latent variables. New York: John Wiley & Sons Publishing.

Bratsberg, Bernt. 1995. Legal versus illegal U.S. immigration and source country characteristics. Southern Economic Journal 61:715-27.

Browne, Michael W., and Robert Cudeck. 1993. Alternative ways of assessing model fit. In Testing structural equation models, edited by Kenneth A. Bollen and J. Scott Long. Newbury Park, CA: Sage, pp. 445 55.

Buehn, Andreas, Alexander Karmann, and Friedrich Schneider. 2009. Shadow economy and do-it-yourself activities: The German case. Journal of Institutional and Theoretical Economics. In press.

Buehn, Andreas, and Friedrich Schneider. 2008. MIMIC models, cointegration and error correction: An application to the French shadow economy. CESifo Working Paper No. 2200.

Carpenter, Ted G. 2005. Mexico is becoming the next Colombia. Cato Institute Foreign Policy Briefing 87:1 8.

Dell'Anno, Roberto. 2007. The shadow economy in Portugal: An analysis with the MIMIC approach. Journal of Applied Economics 10:253-77.

Dell'Anno, Roberto, and Friedrich Schneider. 2003. The shadow economy of Italy and other OECD countries: What do we know? Journal of Public Finance and Public Choice 21:97 120.

Dell'Anno, Roberto, and Friedrich Schneider. 2006. Estimating the underground economy: A response to T. Breusch's critique. Johannes Kepler University Linz, Department of Economics Working Paper 06/07.

Dell'Anno, Roberto, and Offiong H. Solomon. 2008. Shadow economy and unemployment rate in USA: Is there a structural relationship? An empirical analysis. Applied Economies 40:2537 55.

Drug Availability Steering Committee. 2002. Drug availability estimates in the United States. Washington, DC: Office of National Drug Control Policy.

Eggerstedt, Harald, Rebecca B. Hall, and Sweder van Wijnbergen. 1995. Measuring capital flight: A case study of Mexico. Worm Development 23:211-32.

Farzanegan, Mohammad R. 2008. Illegal trade in the Iranian economy: Evidence from a structural model. CESifo Working Paper No. 2397.

Fausten, Dietrich K., and Brett Pickett. 2004. Errors & omissions in the reporting of Australia's cross-border transactions. Australian Economic Papers 43:101-15.

Fisman, Raymond, and Shang-Jin Wei. 2007. The smuggling of art, and the art of smuggling: Uncovering the illicit trade in cultural property and antiques. NBER Working Paper No. 13446.

Fleck, Susan, and Constance Sorrentino. 1994. Employment and unemployment in Mexico's labor force. Monthly Labor Review 117:3 31.

Ford, Jess T. 2008. U.S. assistance has helped Mexican counternarcotics efforts, but the flow of illicit drugs into the United States remains high. Washington, DC: U.S. Government Accountability Office.

French, Michael T., M. Christopher Roebuck, and Pierre K. Alexandre. 2001. Illicit drug use, employment, and labor force participation. Southern Economic Journal 68:349 68.

Hanson, Gordon H., and Antonio Spilimbergo. 1999. Illegal immigration, border enforcement, and relative wages: Evidence from apprehensions at the U.S.-Mexico border. American Economic Review 89:1337-57.

Hanson, Gordon H. 2006. Illegal migration from Mexico to the United States. Journal of Economic Literature 44:869-924.

Hoefer, Michael, Nancy Rytina, and Bryan C. Baker. 2008. Estimates of the unauthorized immigrant population residing in the United States." January2007. Washington, DC: U.S. Department of Homeland Security Office of Immigration Statistics.

International Monetary Fund (IMF). 1993. A guide to direction of trade statistics. Washington, DC: International Monetary Fund.

Johnston, Lloyd D., Patrick M. O'Malley, Jerald G. Bachman, and John E. Schulenberg. 2007. Monitoring the future national survey results on drug use. 19752006. Volume l: Secondary, school students, NIH Publication No. 07-6205. Bethesda, MD: National Institute on Drug Abuse.

Joreskog, Karl G. 1970. A general method for analysis of covariance structures. Biometrika 57:239-51.

Martin, Lawrence, and Arvind Panagariya. 1984. Smuggling, trade and price disparity: A crime-theoretic approach. Journal of International Economics 17:201-17.

McDonald, Donogh C. 1985. Trade data discrepancies and the incentive to smuggle. IMF Staff Paper 4:668-92.

Norton, Desmond A. G. 1988. On the economic theory of smuggling. Economica 55:107-18.

Office of Border Patrol. 2004. "National border patrol strategy." Accessed 24 November 2008. Available http://www.cbp.gov.

Passel, Jeffrey S., and D'Vera Cohn. 2008. Trend in unauthorized immigration: Undocumented inflow now trails legal inflows. Washington, DC: Pew Hispanic Center.

Pick, Franz. 1955-1982. Pick's currency yearbook, Various issues. New York: Pick Publishing Corporation,

Pick, Franz. 1983-1998. Worm Currency Reports, Various issues. New York: International Currency Analysis Inc.

Pitt, Mark M. 1981. Smuggling and price disparity. Journal of International Economics 11:447 58.

Pitt, Mark M. 1984. Smuggling and the black market for foreign exchange. Journal of International Economics 16:243-57.

Pohit, Sanjib, and Nisha Taneja. 2003. India's informal trade with Bangladesh: A qualitative assessment. The Worm Economy 26:1187-214.

Rhodes, William, Mary Layne, Anne-Marie Bruen, Patrick Johnston, and Lisa Becchetti. 2001. What America's users spend on illegal drugs. Washington, DC: Office of National Drug Control Policy.

Schneider, Friedrich. 2005. Shadow economies around the world: What do we really know? European Journal of Political Economy 21:598-642.

Schneider, Friedrich, and Dominik Enste. 2000. Shadow economies: Size, causes, and consequences. The Journal of Economic Literature 38:77 114.

Schneider, Friedrich, and Dominik Enste. 2002. The shadow economy: Theoretical approaches, empirical studies, and political implications. Cambridge, UK: Cambridge University Press.

* Faculty of Business and Economics, Technische Universitaet Dresden, Chair for Economics, esp. Monetary Economics, 01062 Dresden, Germany: E-mail [email protected]: corresponding author. [dagger] Faculty of Business and Economics, Technische Universitaet Dresden, Chair for Economics, esp. Monetary Economics, 01062 Dresden, Germany; E-mail [email protected]. We thank Gordon Hanson for providing the data on Mexican wages and U.S. border enforcement. We are also grateful to Alexander Karmann, Sunshine Moore, the editor, and two anonymous referees for their many useful comments and suggestions on this article. We also benefited from comments of participants of the Lunchtime Seminar at Technische Universitaet Dresden. All remaining errors are the authors' responsibility.

Received July 2008; accepted January 2009.

(1) MIMIC approaches were previously applied to estimate the development of the shadow economy (see, for example, Dell'Anno and Schneider [2003]; Schneider [2005]: and Dell'Anno [2007]). A comprehensive overview of such studies is provided in Schneider and Enste (2000, 2002).

(2) Analogously, export underinvoicing (overinvoicing) occurs in the exporting country if the export figures of the exporting country fall short of (exceed) the import figures of the importing country.

(3) Biswas and Marjit (2007) use a similar approach to study the rationale for trade misinvoicing.

(4) The exchange rate, e, is defined as the price of 1 $U.S. in terms of Mexican pesos. Thus, a rise in the exchange rate corresponds to a depreciation of the peso against the dollar.

(5) Until 2003, the U.S. Customs Service. !!! BEGIN AUTH-ABST

(6) Per definition, v > - 1 holds, and thus, d[S.sup.ill]/d[epsilon] > 0 generally applies.

(7) We define misinvoicing as underinvoicing, that is, as the difference between the actual and the reported export/import figures. Defining misinvoicing as overinvoicing would just reverse the theoretical hypotheses.

(8) The variable t denotes the Mexican profit/income tax. Obviously, only legal transactions are subject to taxation. For simplicity, we do not consider any production or procurement costs.

(9) [dS.sup.x]/dv > 0 is true, as v + t > 0 holds in our sample.

(10) The profit-maximizing Mexican importer focuses on minimizing costs. Underinvoicing imports, [S.sup.M] > 0, therefore means cutting back on legal expenditures (1 - t)(1 + q)[epsilon][S.sup.M] but increasing illegal expenditures (1 + v)[epsilon][S.sup.M]. Thus, the importer underinvoices if avoided legal costs exceed additional illegal costs, (1 - t)(1 + q) - (1 + v) > 0.

(11) Joreskog (1970) first introduced structural equation models into economics.

(12) A similar presentation of the MIMIC methodology can be found in Buehn and Schneider (2008) and Buehn, Karmann, and Schneider (2009).

(13) The export figures are in FOB (Free on Board) prices, and the import figures are in CIF (Cost, Insurance, and Freight) prices. In order to make them comparable, we divide the export figures by an adjustment factor of 1.1, as suggested by the International Monetary Fund (IMF 1993), taking into account transport and insurance costs.

(14) In addition to trade misinvoicing, errors and omissions reflect misreporting of capital flows and different schedules for reporting goods in transit (see, for example, Fausten and Pickett [2004]). However, trade misinvoicing is a popular instrument to camouflage capital flight, and therefore, we assume the size of errors and omissions to be mainly driven by trade misinvoicing (Eggerstedt, Hall, and van Wijnbergen 1995).

(15) The unit root test results are available upon request. We also tested for cointegration between I(l) indicators and the corresponding causes but could not confirm any unambiguous cointegration relation.

(16) All calculations have been carried out with LISREL[R] Version 8.80. Tables 2 and 3 show the unstandardized coefficients, which are used in section 6 to calculate the indices for illegal and legal goods smuggling. As a robustness check, we also calculate these indices using standardized coefficients. Neither the estimation results nor the calculated indices are sensitive to the choice of coefficients.

(17) The choice of the indicator to fix the scale of the latent variable does not affect the results.

(18) To calculate the smuggling indices in section 6, we use the fixed indicator as an index variable, the value of which is expressed relative to the base year value. Linewatch apprehensions are therefore used as an index variable equal to (linewatch apprehensions at t)/(linewatch apprehensions 2000), while errors and omissions are used as an index equal to (errors and omissions at t)/(errors and omissions 1984).

(19) We could not estimate specification 3 by varying the set of indicators because the variable drug availability still exhibits a unit root for 1980-1998, even after taking the first difference.

(20) According to expert estimates shown in Table 5, most of the cocaine and marijuana available in the United States is smuggled via the Mexican border.

(21) [x.sub.1t], [x.sub.2t], and [x.sub.3t] represent the unemployment rate, real wages, and border enforcement, respectively.

(22) As outlined in section 6, linewatch apprehensions are used as an index variable, where the denominator equals linewatch apprehensions in the base year 2000. As the latent variable is measured in units of the fixed indicator, illegal goods smuggling is measured per apprehended smuggler at the border in 2000.

(23) Specifications 1 through 3 cannot be used as they do not cover the base year 2000.

(24) The pattern of the illegal goods smuggling index is not dominated by one or two of the causes; although, the variable "probability of apprehension" has a large coefficient and thus influences the dynamics the most.

(25) The U.S.-Mexico case seems to be especially relevant in our context, as illegal immigration is typically more likely the poorer and the less distant the source country (see, for example, Bratsberg [1995]).

Table 1. Review of the Empirical Literature on Trade Misinvoicing

Study Subject of Investigation

Bhagwati Import
(1964) underinvoicing
 in Turkey
McDonald Incentives for
(1985) export
 misinvoicing
Pohit and Informal trade
Taneja between
(2003) India and
 Bangladesh
Fisman and Illicit trade in
Wei (2007) cultural
 properties
 in the
 United States
Beja (2008) Trade
 misinvoicing
 in China
Berger and Bilateral trade
Nitsch discrepancies
(2008) at the 4-digit
 product level
Farzanegan Illicit trade
(2008) in Iran

Study Approach

Bhagwati Descriptive analysis of trade
(1964) from Turkey to its major
 trading partners: France,
 Germany, Italy, the
 Netherlands, and
 the United States
McDonald Ordinary least squares (OLS)
(1985) regressions for 10 developing
 countries; dependent
 variable: trade discrepancies;
 independent variables: BMP
 and export taxes
Pohit and Direct survey approach
Taneja encompassing 100 traders
(2003) in each country
Fisman and Worldwide unbalanced panel
Wei (2007) for 1996-2005; dependent
 variable: trade discrepancies
 in cultural object and
 antiques; independent
 variables: corruption,
 GDP per capita, dummies
Beja (2008) Descriptive analysis of trade
 discrepancies
Berger and OLS regressions for
Nitsch misinvoicing in bilateral
(2008) trade with the United States,
 Germany, China, the United
 Kingdom, and Japan;
 dependent variable: trade
 discrepancies; independent
 variables: corruption,
 GDP per capita, distance
 measure, dummy variables
Farzanegan MIMIC approach; causes:
(2008) fines, black market and
 official exchange rate,
 unemployment rate, tariffs;
 indicators: government
 revenues, import price
 index, BMP, petroleum
 consumption

Study Main Findings

Bhagwati Import underinvoicing in
(1964) transport equipment
 and machinery
McDonald Mediocre statistical
(1985) evidence that the BMP
 and export taxes
 explain variations in
 trade discrepancies
Pohit and Anonymous trading
Taneja transactions
(2003) characterize informal
 trade; motivations are
 the quick realization of
 payments, less
 paperwork, and
 procedural delay
Fisman and Highly positive
Wei (2007) correlation between
 trade discrepancies and
 corruption (i.e., more
 corrupt countries are
 more likely to
 misreport data)
Beja (2008) Trade misinvoicing
 occurs mainly between
 Hong Kong and the
 United States
Berger and Trade discrepancies
Nitsch differ widely across
(2008) importers; export
 underinvoicing
 is prevalent in antiques
 and bulky products;
 strong positive
 correlation with
 corruption in the
 source country
Farzanegan Illicit trade is related
(2008) positively to tariffs and
 negatively to fines and
 the unemployment
 rate; adverse effects on
 government revenues,
 the import price index;
 variation between 6%
 and 25% of total trade
 (1970-2002)

Table 2. MIMIC Model Estimations for Illegal Goods Smuggling

 Specification

 1 2
Time Period
 1975-1998 1975-1998
Causes
 BMP (through 1998) .02 (.99) .02 (.99)
 Real exchange rate -.02 (-.80) -.02 (-.57)
 Unemployment rate .05 ** (2.20) .05 *** (2.34)
 Real wages -.03 ** (-2.26) -.05*** (-3.25)
 Border enforcement -2.02 *** (-16.11) -2.01 *** (-16.27)
Indicators
 Linewatch
 apprehensions (fixed) 1.00
 Non-linewatch
 apprehensions 1.02***(9.33) 1.03 *** (9.23)
 Drug seizures .12 ***
 Drug availability .02 (.58)
Goodness-of-fit indices
 Observations 282 282
 Degrees of freedom 25 25
 Chi-square (P-value) 5.27 (.99) 14.88 (.94)
 RMSEA .00 .00

 3 4
Time Period
 1980-1998 1975-2004
Causes
 BMP (through 1998) -.01 (-.61)
 Real exchange rate -.02 (-.68) 0.02
 Unemployment rate .05 ** (2.24) .05 * (1.69)
 Real wages -.05 *** (-3.18) -.05 * (-1.91)
 Border enforcement -2.05 *** (-15.87) -.64 *** (-9.15)
Indicators
 Linewatch
 apprehensions (fixed) 1.00
 Non-linewatch
 apprehensions 1.09 *** (9.57) .49 *** (13.66)
 Drug seizures .09 * (1.68) .00 (.05)
 Drug availability
Goodness-of-fit indices
 Observations 223 358
 Degrees of freedom 25 18
 Chi-square (P-value) 2.79 (.97) 5.22 (.99)
 RMSEA .00 .00

 5 6
Time Period
 1975-2004 1980-2004
Causes
 BMP (through 1998)
 Real exchange rate .02 (.44) .03
 Unemployment rate .05 * (1.73) .06 ** (2.00)
 Real wages -.05 ** (-2.20) -.06 *** (-2.36)
 Border enforcement -.63 *** (-9.18) -.63 *** (-9.01)
Indicators
 Linewatch
 apprehensions (fixed) 1.00 1.00
 Non-linewatch
 apprehensions .50 *** (13.34) .48 *** (13.34)
 Drug seizures .00 (.08)
 Drug availability .04 (.75)
Goodness-of-fit indices
 Observations 358 300
 Degrees of freedom 18 18
 Chi-square (P-value) 9.96 (.93) 4.91 (.99)
 RMSEA .00 .00

 7
Time Period
 1980-2004
Causes
 BMP (through 1998)
 Real exchange rate .02
 Unemployment rate .07 ** (2.05)
 Real wages -.06 *** (-2.67)
 Border enforcement -.61 *** (-8.99)
Indicators
 Linewatch
 apprehensions (fixed) 1.00
 Non-linewatch
 apprehensions .49 *** (12.95)
 Drug seizures
 Drug availability .04 (.76)
Goodness-of-fit indices
 Observations 300
 Degrees of freedom 18
 Chi-square (P-value) 9.34 (.95)
 RMSEA .00

z-statistics in parentheses. If the model fits the data
perfectly and the parameter values are known, the sample
covariance matrix equals the covariance matrix implied by the model
[i.e., S = [SIGMA]([theta])]. The null hypothesis of perfect fit
corresponds to a p-value of I . The root mean squared error of
approximation (RMSEA) measures the model's fit based on the difference
between the estimated and the actual covariance matrix. RMSEA values
smaller than 0.05 indicate a good fit (Browne and Cudeck 1993).

* Significance at the 10% level.

** Significance at the 5% level.

*** Significance at the 1% level.

Table 3. MIMIC Model Estimations for Legal Goods Smuggling

Export Misinvoicing

Specification
 8 9
Time Period
 1980-1998 1980-2004
Causes
 BMP (through 1998) -.02 (-.46)
 Real exchange rate .16 *** (2.82) .17 *** (3.52)
 Taxes on income/profit .11 *** (2.54) .14 *** (3.15)
 Taxes on international
 trade
Indicators
 Errors and omissions
 (fixed) 1.00 1.00
 Import misinvoicing
 Export misinvoicing .19 (.52) .06 (.19)
Goodness-of-fit indices
 Observations 228 305
 Degrees of freedom 8 4
 Chi-square (p-value) 1.85 (.98) .91 (.92)
 RMSEA .00 .00

Import Misinvoicing

Specification
 10 11
Time Period
 1980-1998 1980-2004
Causes
 BMP (through 1998) -.01 (-.27)
 Real exchange rate -.13 *** (-2.45) -.16 *** (-3.45)
 Taxes on income/profit -.10 *** (2.79) -.13 *** (-3.24)
 Taxes on international
 trade .06 ** (1.96) .06 * (1.68)
Indicators
 Errors and omissions
 (fixed) -1.00 -1.00
 Import misinvoicing .17 (.67) .23 (.97)
 Export misinvoicing
Goodness-of-fit indices
 Observations 228 305
 Degrees of freedom 9 8
 Chi-square (p-value) 5.38 (.80) 1.74 (.98)
 RMSEA .00 .00

z-statistics in parentheses. If the model fits the data perfectly and
the parameter values are known, the sample covariance matrix equals
the covariance matrix implied by the model [i.e., S = E(8)]. The null
hypothesis of perfect fit corresponds to a p-value of 1. RMSEA
measures the model's fit based on the difference between the estimated
and the actual covariance matrix. RMSEA values smaller than 0.05
indicate a good fit (Browne and Cudeck 1993).

* Significance at the l0% level.

** Significance at the 5% level.

*** Significance at the 1% level.

Table 4. Employment Characteristics of an Average Illegal Mexican
Immigrant during Her Stay in the United States

Duration in the
United States Months Worked Hours Worked
(in Months) per Year per Week

20.08 9.41 46.51

Duration in the
United States Hourly Wage Illegal Wages Earned in the
(in Months) (in $U.S.) United States (in $U.S.)

20.08 8.62 26,325

Source: Mexican Migration Project (MMP) database. The MMP data are
available online at http://mmp.opr.princeton.edu.

These average characteristics are drawn from a subsample of 270 survey
respondents who entered the United States illegally, that is, with or
without false documents, between 2000 and 2006.

Table 5. Base Value for Illegal Drugs Smuggled across U.S.-Mexico
Border in 2000

 Cocaine Heroin

Total U.S. expenditures on
 illegal drugs in 2000
 (in billion $U.S.) (a) 35.3 10.0
Estimated average percentage
 arriving in the United States
 through U.S.-Mexico border 66 (b) 18 (c)
Estimated value of illegal drugs
 smuggled through the U.S.-Mexico
 border in 2000 (in billion $U.S.) 23.3 1.8

 Marijuana Methamphetamine

Total U.S. expenditures on
 illegal drugs in 2000
 (in billion $U.S.) (a) 10.5 5.5
Estimated average percentage
 arriving in the United States
 through U.S.-Mexico border 55.6 (d) 9.1 (e)
Estimated value of illegal drugs
 smuggled through the U.S.-Mexico
 border in 2000 (in billion $U.S.) 5.8 0.5

 Total

Total U.S. expenditures on
 illegal drugs in 2000
 (in billion $U.S.) (a) 61.2
Estimated average percentage
 arriving in the United States
 through U.S.-Mexico border
Estimated value of illegal drugs
 smuggled through the U.S.-Mexico
 border in 2000 (in billion $U.S.) 31.4

(a) Source: Rhodes et al. (2001, p. 31).

(b) The Interagency Assessment of Cocaine Movement estimates that 66%
of cocaine in the United States flows through Mexico (Ford 2008, p. 7).

(c) According to the Drug Availability Steering Committee (2002,
p. 61), 16-20% of heroin in the United States in 2000 originated in
Mexico.

(d) The Drug Availability Steering Committee (2002, p. 106, 119)
estimates that 4651 metric tons of Mexican marijuana arrived on the
U.S. market in 2000. The total amount of marijuana in the United
States in 2000 is estimated at between 5577 and 16,731 metric tons,
which corresponds to a Mexican market share of between 27.8% and
83.4%.

(e) According to the Drug Availability Steering Committee (2002,
pp. 82-5), 8.6-9.6% of methamphetamines in 2000 came from Mexico.