Estimation of the Timing Asymmetry in International Trade
  • 1 0000000404811396 Monetary Fund

Because of the time involved in transporting goods between countries and in fulfilling certain customs requirements, the export shipments of a country or region during a given period will not all be received and counted as imports by trading partners during the same period. It follows that, apart from differences in coverage and the basis of valuation (for example, f.o.b. or c.i.f.), the value of a region’s exports will necessarily exceed the value of partners’ imports from it if international trade is increasing, and the converse will be true if trade is declining. Moreover, the discrepancy between exporter–reported and importer–reported values will tend to vary directly with the size of the increase or decrease. In this paper, the lag between the recording of goods as exports and the recording of the same goods as imports is called the transport lag. The discrepancy between exporters’ and importers’ merchandise accounts for a given period that is to be expected because of the transport lag is called the timing asymmetry. 1


Because of the time involved in transporting goods between countries and in fulfilling certain customs requirements, the export shipments of a country or region during a given period will not all be received and counted as imports by trading partners during the same period. It follows that, apart from differences in coverage and the basis of valuation (for example, f.o.b. or c.i.f.), the value of a region’s exports will necessarily exceed the value of partners’ imports from it if international trade is increasing, and the converse will be true if trade is declining. Moreover, the discrepancy between exporter–reported and importer–reported values will tend to vary directly with the size of the increase or decrease. In this paper, the lag between the recording of goods as exports and the recording of the same goods as imports is called the transport lag. The discrepancy between exporters’ and importers’ merchandise accounts for a given period that is to be expected because of the transport lag is called the timing asymmetry. 1

Because of the time involved in transporting goods between countries and in fulfilling certain customs requirements, the export shipments of a country or region during a given period will not all be received and counted as imports by trading partners during the same period. It follows that, apart from differences in coverage and the basis of valuation (for example, f.o.b. or c.i.f.), the value of a region’s exports will necessarily exceed the value of partners’ imports from it if international trade is increasing, and the converse will be true if trade is declining. Moreover, the discrepancy between exporter–reported and importer–reported values will tend to vary directly with the size of the increase or decrease. In this paper, the lag between the recording of goods as exports and the recording of the same goods as imports is called the transport lag. The discrepancy between exporters’ and importers’ merchandise accounts for a given period that is to be expected because of the transport lag is called the timing asymmetry. 1

This paper presents a method for estimating the lag and the corresponding asymmetry indirectly, on the basis of differences between the exporter and importer records of trade values. The primary use of the results occurs in comparisons of world aggregates of exports and imports. If the aggregates are of historical data, one is interested in how much of the apparent discrepancy is explainable on the basis of the lag. 2 If the figures are for future periods, a forecast of the total trade asymmetry provides a measure of the difference to be expected between global export and import forecasts, as a check on their consistency. The timing asymmetry is only a part of this discrepancy. However, evidence to be presented later suggests that it is a substantial and, in recent years, highly variable part. After subtracting the estimated timing asymmetry, the residual asymmetry on world trade account becomes relatively smooth and is therefore itself not difficult to forecast. Estimates of these asymmetry components are given in Table 1 for the years 1967–77.3

Table 1.

Values of the “World” Trade Account Asymmetry and Estimated Components, 1967–77 1

(In billions of U. S. dollars)

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“World” is defined to be members of the International Monetary Fund (IMF) that report data plus certain nonmembers (including Switzerland and Hong Kong but excluding the so–called Sino–Soviet countries and other countries that do not report balance of payments statistics to the IMF).

These data are from the IMF Data Fund as of February 1979. Except for revisions and conversion from special drawing rights to U. S. dollars, they are the same as those in line 1, Table A–1 of IMF, Balance of Payments Yearbook, 1971–77: Supplement to Volume 29 (December 1978). For both exports and imports, valuation is f.o.b. and coverage is balance of payments basis as far as practicable.

If the timing asymmetry has been estimated with reasonable accuracy, the residual is attributable to asymmetries of valuation and coverage. Numerous hypotheses exist regarding the sources of such discrepancies. (See, for example, Smith, “Asymmetries and Errors in Reported Balance of Payments Statistics,” cited in footnote 1 in the text.) Two of the more general hypotheses, which are also consistent with the observed surplus of recorded credits, are (1) that relatively higher tariffs borne by imports create pervasive incentives for underreporting of import values, and (2) that actual freight charges below the conventional 10 per cent rule of thumb imply overimputation of the c.i.f. component, and thus result in underrecording of merchandise debits and overrecording of service debits in balance of payments statistics.

The figures cover countries not included in the “world” as defined in footnote 1. Besides the Sino–Soviet area, the group includes seven independent countries and nine territories–principally Brunei, Angola, and Mozambique. The figures have been estimated on the basis of partner–country reports in Direction of Trade. Territories in addition to these appear in Direction of Trade, but their trade is already included in the balance of payments statistics of the respective metropolitan areas.

Preliminary figures.

Another use of the transport lag calculations relates to the evidence they contain regarding the currency in which foreign trade invoices are denominated. Several recent studies suggest that the typical practice is use of the currency of either the exporter or the importer. 4 While only indirect evidence on this point is provided here, it is based on a broad sample—namely, world trade. By contrast, the existing direct assessments of the currency denomination of trade contracts are based on samples of individual invoices, and in any case, the practices of only a few countries have been studied.

I. Basic Model

Let Xt be defined as the value of exports of Region A to Region B in period t as recorded by Region A, and let Mt be imports of Region B from A as recorded by B. If there were no differences of valuation, timing, or coverage, one would observe that A = Xt in each period.

The coefficients bi, i = 0, 1, …, are defined to be the proportions of Xt that are not received and counted as imports until period t + i. The bi are assumed to be constant over time. Also assumed constant are the parameters a, the ratio of the value of costs, insurance, and freight to the value of exports at the exporter’s border, and k, the average value of net trade between Regions A and B that is misclassified as to origin or destination. Instead of Mt = Xt, the relation is


The assumption of constant parameters is better satisfied the more stable are the distributions of regional trade flows (1) over individual importing and exporting countries of unequal distance from partner regions, (2) over commodities having dissimilar ratios of freight charges to value, and (3) over modes of transportation (air or surface carriers).

Apart from recording errors, discussed later, all exports are eventually counted as imports. It is therefore appropriate to constrain the bi to equal unity. Substituting for b0 according to


one may rewrite equation (1) as


For annual data, equation (2) simplifies to


since on the basis of extraneous information, such as shipping schedules, it is apparent that the average lag is likely to be a small fraction of a year. Regression analysis will not yield estimates of the parameters of equation (2) directly, but rather of the ci in


However, by inspection, the structural parameters are seen to be exactly identified and may be derived as follows: 5


In practice, equation (2) will be affected by recording errors and omissions, which may be large for certain countries. To the extent that such errors tend to be proportional to the recorded value of trade, as is likely, the estimates of the ci will be biased. It follows that the structural parameter a will reflect some combination of freight and insurance payments and recording errors, and its interpretation must be modified correspondingly. But the estimates of the bs, which are of primary interest here, tend to be unaffected by such errors. Since the estimates of the coefficients ci will be biased to the same proportional extent, this influence will cancel in computing the b^i. (See equation (5″).) Thus, inclusion of a in the specification serves to separate the proportional discrepancy between importer and exporter data from the lag between the two versions so that the latter can be estimated. 6

Estimates of the bi will be affected by recording errors that are proportional to the change in the trade flow. This would occur, for example, if the officials in a particular customs post have an uneven work load such that incoming shipments are very heavy toward the end of each month and a fraction of these are regularly left unprocessed till the beginning of the following month. Such effects as these, however, have been included, by definition, in the timing asymmetry. In light of the applications mentioned earlier, it is appropriate to measure the actual lag in the published data irrespective of whether it is attributable solely to “transport” or includes customs delays as well.

The value of the asymmetry itself, At, is logically defined to be the difference between recorded exports and imports after both are placed on the same basis of valuation and coverage. If imports are converted to “export” basis,


then the asymmetry is given by


or, for annual data, by b · ΔXt.

The length of the lag expressed in units of time can only be approximated from the regression results. For example, suppose the period of observation is a month. Shipments both exported and imported in the same month can have a lag, at one extreme, of zero days (if sent by air, or across a common land boundary) or, at the other extreme, of about 30 days. If it is reasonable to assume that, within a month, the lags of individual shipments are distributed uniformly between these two extremes, then shipments exported on the first day and imported during the same month will have a mean lag of about 15 days, or 0.5 month. This mean applies only to shipments exported at the very beginning of the month. A lag of zero obtains, at the other extreme, to shipments exported on the last day of the month and imported on the same day. The mean, in turn, of this second pair of two extremes–0.25 month—may be taken as a crude approximation of the average lag of all shipments exported and imported during the same month. Applying this reasoning to shipments imported i months after the month of exportation, one derives the following expression for the mean lag:


This formula is used later for results based on monthly data. Whether or not it provides a good approximation cannot be determined without data of higher frequency. However, it is very likely superior to the assumption of an average lag of zero for shipments exported and imported in the same month. In any case, expression of the lag in terms of time units is of secondary interest, as the simulations of the asymmetry are based on the b^i and are independent of L.

II. Exchange Rate Effect

For this study, it is necessary to express all countries’ trade flows in terms of a single currency, for which purpose the U.S. dollar is the convenient choice. However, to the extent that world trade is not invoiced in U.S. dollars (as suggested by Grassman and Magee in their works cited in footnote 4), and the dollar is depreciating against other currencies on average, the customs value in dollars of a particular shipment will be higher on arrival than at departure because of exchange rate movements during transit. Conversely, if the U.S. dollar is appreciating, the customs value will, in effect, fall somewhat during transit. This factor will tend to create a systematic difference between importer and exporter records expressed in dollars, especially for recent years. It is appropriate to modify the basic model to allow for such exchange rate effects.

If all shipments were in transit precisely one month, the maximum exchange rate effect for a single pair of trading countries would be equal to the monthly proportionate exchange rate change times the monthly export value lagged one period, this quantity summed over the months in the period of observation. Thus, for annual data, the effect, Rt, would be written (where X is exports and r* is the proportionate change in the exchange rate expressed in terms of dollars per unit of exporter’s currency)


For an exporting region of n countries, r in the preceding expressions would be replaced by a suitably weighted average exchange rate. Addition of the exchange rate effect to the annual version of the model yields


The coefficient d may be interpreted as the proportion of trade invoiced in currencies other than the U. S. dollar and other than those pegged to the dollar.

The foregoing development holds for annual or quarterly data, but if a monthly version of the model is estimated, the assumption of a uniform one–month transport lag is unnecessary. The import record in period t of goods exported i months ago is increased approximately by the factor d (rt/rt-i – 1) where, as earlier, d is the proportion of exports not denominated in dollars. Based on equation (2), the monthly model including the exchange rate effect may thus be written


utilizing the substitutions



Equation (9) is overdetermined but can be estimated by use of nonlinear methods.

III. Econometric Approach

The bilateral trade data appearing in the IMF publication, Direction of Trade (DOT), are appropriate for estimating the model developed earlier, in that time series of both importer and exporter records are available for any desired degree of geographical disaggregation. During a period in which the trade flows of various groups of countries grow at unequal rates, such as recent years, it may be possible to improve estimates substantially by dividing the world into more homogeneous regions, estimating the transport lag for each separately, and reaggregating the asymmetry simulations to obtain the desired world total. On the other hand, DOT provides only annual data. Higher frequency series—in particular, monthly data—are not generally available for countries outside the industrial group. (So–called derived entries can be generated, but these are not useful for present purposes, as discussed later in this section.) Estimates based on monthly data are desirable from the point of view of precision, since the transport lag is short relative to a year. Such monthly data as do exist, from the summary tables at the front of the IMF publication, International Financial Statistics (IFS), are available from both exporter and importer records only for the world as a whole. 8 The availability of data thus imposes a choice between disaggregation into regions and “disaggregation” into shorter units of time.

The alternative based on annual data is pursued first, as there is a presumption of potentially large differences in the transport lag among geographical areas. The annual data samples are found to yield lag estimates implying a global average rather larger than the traditional one–month rule of thumb. These plausible results are, nevertheless, ultimately rejected. First, interregional differences among the estimates are found to be surprisingly slight, at least for the regional breakdown chosen for the study. Second, the estimates are seen to be peculiarly vulnerable to collinearity, which is present among the relevant annual series to an extreme degree, particularly because of large rates of growth of trade values in the early 1970s. The regional disaggregation is therefore discarded, and the transport lag is re-estimated with the monthly data available for the world as a whole. These latter series yield an estimate of the lag that is substantially shorter than the traditionally assumed magnitude, and direct evidence on transportation lags is cited as a check on the results.

As suggested by the first alternative, estimates of the transport lag based on annual data have been prepared for the four–way regional disaggregation of world trade that is used in IMF data publications: industrial countries, more developed primary producing countries, oil exporting countries, and other (“non–oil”) developing countries. 9 Being partly structural, this grouping is at least similar to what one would devise for convenience in organizing or summarizing a comprehensive trade–forecasting effort. Results based on a second, five–way, purely geographical, disaggregation are mentioned later. The potentially more uniform distances between importing and exporting countries of this second grouping will tend to yield regression coefficients with smaller margins of error, other things being equal. Estimates of the transport lag have been calculated both for the exports of these two groups of regions to the world and for exports to other regions individually, as well as for world trade in the aggregate. 10

Two special considerations apply to estimates based on annual DOT data. The first is the presence of so–called derived statistics—the use of partner–country figures for missing bilateral entries. The associated regression estimates of the transport lag are biased toward zero (use of the same record for X and M implies no lag), and the c.i.f. factors are biased toward 10 per cent (the proportion assumed in converting the available record from f.o.b. basis to c.i.f., or the other way around). The incidence of derived data is zero or nil for all regions except the oil exporting countries, in which case a degree of error as large as one third of the regression estimate is not unlikely. Consequently, for the oil region, an a priori estimate of the transport lag of one month has been substituted in the annual–data simulations of the timing asymmetry reported later. 11

The second special consideration is a consequence of the likelihood, in the light of extraneous information, that the transport lag is much shorter than a year. In this case, export developments in the early months and quarters are irrelevant from the point of view of the lag, as most of this trade will be imported in the same year in which it is exported. The term ΔXt in the model—equation (3)—is thus a proxy for the year–on–year difference in export developments occurring toward the end of the year, the only portion of the yearly flow that is potentially caught in the float. Consequently, the estimate of b can be improved, in principle, by replacing ΔXt by (… + Xt:Nov Xt:Dec … Xt – 1:Nov Xt – 1:Dec), and adjusting the scale of b^ accordingly. 12

The precise number of end–year months to be included in this term cannot be determined analytically, but whatever error may be introduced by making an incorrect a priori judgment is likely to be much smaller than that caused by using the annual proxy. The smaller the number of months included, the greater is the risk of excluding shipments with long lags; 13 the larger the number of months, the greater the amount of irrelevant variation that is introduced. The final three months comprise the subperiod used here. 14 This variant of the annual–data equation is labeled end–year in the description of results that follows.

The regression results calculated from samples of annual data for the four–way disaggregation of world trade are shown in Table 2. The estimation is based on samples ending in 1974 because the published data for succeeding years are subject to revision. While the magnitude of further revisions is likely to be small—not exceeding 1 to 2 per cent—only the import series is affected; export revisions are negligible. As the differences between global exports and imports are inherently slight, spurious discrepancies of an additional couple of percentage points may have a sizable effect on the calculated estimates. Coefficients of variation are reported in place of coefficients of multiple correlation in Table 2; the latter are uniformly very high. The table shows that the standard errors of the regressions lie between about ½ of 1 per cent and 1½ per cent of the means of the respective dependent variables, except for oil exporting countries. The hypothesized exchange rate effect is not supported by the annual data, as may be seen in part (b) of Table 2. The coefficient on the exchange rate variable has the incorrect sign for exports of the industrial countries and the more developed primary producing countries. These two groups together account for 75 per cent of world trade over the sample. 15 As for the parameters of primary interest, the estimates of a and b for the end–year are all of reasonable magnitude, and the t–ratios are generally high. (Since the estimates of b are nonlinear, and only large–sample standard errors are known, their statistical significance cannot be judged, strictly speaking.)

Table 2.

Regression Estimates of the Transport Lag Equation for Regions’ Exports to the World, Based on Annual Data, 1959–74 1

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The coefficient of variation was computed as the ratio of the standard error of the regression (corrected for degrees of freedom) to the mean of the dependent variable. The constant term, k^, is in millions of U. S. dollars. The statistic, b^y is the regression estimate of b re-expressed as a proportion of a year’s trade. Figures in parentheses are t–values. For b^, which is nonlinear, only the large sample standard error can be computed; the t–test of statistical significance does not apply, strictly speaking. The nonlinear algorithm used to estimate the structural parameters was provided by Data Resources, Inc.

The choice between results based on annual data and on end– year data—parts (a) and (c) in Table 2—is not an empirical matter but one of a priori specification. As discussed, the latter set is taken to be more efficient, and thus preferable, on logical grounds. Actual differences between them are slight, however, except that the lag for the non–oil developing region is reduced in the preferred version (again omitting the major oil exporters).

The most striking result is that the estimates of b are so nearly the same across regions. Lying between 0.32 and 0.46 of fourth– quarter trade (again excluding the estimate for oil exporters), or between 0.08 and 0.13 of the yearly flow (final column, included for comparison with parts (a) and (b) of the table), the estimates of b imply a transport lag that is highly uniform. This conclusion depends in part on the foregoing judgment that use of end–year (fourth–quarter) differences in place of ΔXt is a superior specification. Since the annual–data asymmetry simulations are accordingly to be based on these end–year lag estimates, and given that the a priori estimate for the oil exporting region—one month—also falls in this range, it follows that such simulations will not be appreciably different from those that would result from assuming no interregional differences in b^.

This is shown explicitly in Table 3. Estimates of the timing asymmetry are presented there on two bases—namely, the sum of estimates for the four regions individually, and direct world estimates that result from aggregating the data series across regions and then estimating a global transport lag. The effect of the regional disaggregation can be seen by comparing these two types of estimate. The differences are clearly small. In particular, they are negligible, compared with those between the world estimates given in Table 3 and the estimates based on monthly data given in Table 1. These simulations demonstrate the first important result of the paper: The data imply relatively unambiguously that the refinements to be made by way of greater geographical disaggregation are, for the transport lag, much less important than the refinements achieved by use of monthly data. In the light of this result, the appropriate course is to dispense with regional disaggregation and to estimate the transport lag with monthly data for the world as a whole.

Table 3.

Annual–Data Estimates of the Timing Asymmetry, 1960 and 1967–77 1

(In billions of U. S. dollars)

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The sample for estimation of the transport lag was 1959–74. See also the footnotes to Table 1.

A further result based on annual data supports this alternative and, at the same time, contains a strong clue as to the econometric basis of the superiority of monthly–data results. This is the set of estimates for flows between pairs of individual regions. Instances of erratically high or low values of both â and b^ together suggest that X and ΔX are highly collinear (b enters the estimating equation with a negative sign). Thus, the greater stability that, in principle, characterizes the more disaggregated estimates is offset by an increased degree of statistical indeterminacy. The disaggregation is fruitless, and an element of doubt arises concerning results based on annual data in general. The estimates of the coefficients for the bilateral flows, for both the four–way and five–way regional disaggregations, are presented in Section D of the Supplementary Notes mentioned in footnote 6.

IV. Estimates from Monthly Data

Regression estimates of the monthly version of the transport lag equation are given in Table 4, both excluding the exchange rate effect (equation (2), part (a) of the table) and including it (equation (9), part (b)). The samples for estimation cover the period January 1959 through December 1975, as the data for subsequent months are subject to revision.

Table 4.

Regression Estimates of the Transport Lag Equation for World Trade, Imposing Various Lags, Based on Monthly Data, January 1959–December 1975 1

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“World” is defined as in Table 1. The coefficient b^0 is calculated as 1Σb^1,i>0. See also footnote 1 to Table 2.

The monthly equations allow for estimation of the monthly pattern of the lag and not just the overall impact at yearly intervals. Table 4 contains results for lag distributions of various numbers of months, as this aspect of the specification cannot be determined prima facie. In these regressions, there is a clear indication that the lag extends over three past periods, judged by the usual criteria of dwindling t–values and erratic signs. 16 Estimates of the coefficients on the first and third lagged periods (b, and b3) are large relative to that on the second (b2). 17 The foreign exchange effect has the correct sign; the value of d^ implies that the proportion of trade invoiced in currencies other than the U.S. dollar (and currencies pegged to it) is about half, although with a large margin of error (discussed later in this section). By the approximation devised in Section I, equation (7), the mean length of the lag is estimated to be 0.57 month if the exchange rate effect is excluded, 0.59 month if included. 18

The lag estimated from monthly data is substantially smaller than that estimated from annual data. This can be demonstrated by calculating, from the monthly results, the value of b, (the implicit coefficient on lagged annual exports). This coefficient will be equal to December exports not imported in December (16.8 per cent, using the results including the exchange rate effect) times the average weight of December in yearly trade (0.094) plus November exports that are imported neither in November nor December (8.8 per cent) times the November trade weight (0.089) plus October exports not arriving until January (8.8 per cent) times the October weight (also 0.089). The value of by implicit in the monthly estimates is thus 3.1 per cent, compared with 9.0 per cent in the annual results. (See the final stub entry in part (c) of Table 2.)

This striking difference constitutes the second basic result of the study. Both the implicit transport lag and the timing asymmetry to be expected in recorded global export and import values would be smaller by two thirds in the estimates based on monthly data than in those computed from annual data. The explanation for the difference has two major parts. 19 First, there is a problem of scale. Had the transport lag turned out to be, say, three months on average (involving perhaps 0.20 of annual exports), a discrepancy of 0.06 (= 0.09 – 0.03) would have been noticeable but not very troublesome. Second, and more important, inspection reveals a very high degree of collinearity between annual values of X and ΔX, the simple correlation coefficient being 0.97. For monthly data, the analogous measure is 0.35. 20 This signals a dramatic improvement in the estimated statistics with respect to discriminating between the timing discrepancy (coefficient b) and the “c.i.f.” discrepancy (coefficient a). For both of these reasons, but especially the latter, the monthly–data results are strongly to be preferred.

A transport lag rather longer than the one estimated here has commonly been assumed, at least by some researchers—typically on the order of a month, in contrast with the present estimate of about 2½ weeks. 21 Nevertheless, the shorter estimate is no less reasonable on a priori grounds. About one fourth of U.S. trade, and as much as one half for European countries, occurs with partner countries having a common border. For the portion of such flows carried overland, the transport lag is necessarily zero days, apart from customs procedures. The lag applying to the balance of this trade (between ports) must be on the order of no more than a few days—a period not appreciably shorter than intracontinental flows between nonadjacent partners. Such very short lags are likely to be typical, for example, of the bulk of intra–European trade, which comprises about one third of world trade. Also contributing to a short average lag is the fact that numerous commodities are shipped by air, even across long intercontinental distances.

Magee (pp. 132–33) reports some direct evidence bearing on this point. Based on his samples of invoices, the mean “transportation” lag for U.S. imports from Japan was 21 days in the fiscal year 1972/73, 14 days for U.S. imports from the Federal Republic of Germany. 22 To these figures must be added estimates of the “entry” lag, since, until 1978, shipments were included in U.S. import data only after customs processing was substantially complete. As the mean entry lag was about two weeks for both countries in 1973, Magee’s samples indicate transport lags (in the sense used here) of about four and five weeks, respectively, for the Federal Republic of Germany and Japan 23—too long to be easily reconciled with the 2½ week regression estimate, even allowing for the incidence of common border trade in global flows. However, for most of the 1960s, the entry lag was much shorter—a matter of a day or two. In those years, importers did not gain custody of goods until their customs obligations had been met. When procedures were relaxed to allow immediate release, first for perishables and later for merchandise in general, traders took increasing advantage of the ten–day grace period for filing forms and paying duties. (This is undoubtedly a factor in Magee’s finding that the entry lag was only one week in 1971, half as long as in 1973, for both countries.) As the entry date became increasingly distant from the timing of the actual flow of foreign goods, the U.S. Census Bureau changed its procedures so that the “importation” date (roughly, when goods arrive in port) now determines when a particular shipment is included in foreign trade statistics. Such shifts in procedures contribute to the unexplained regression residuals in this study, and in some contexts would merit explicit attention. Moreover, even had U.S. practice remained unchanged during the sample period, it would be no more than suggestive of what other countries may do. But at least Magee’s direct estimates of transport lags for particular transoceanic flows are not inconsistent with the global average estimated here by regression.

The estimates of a—the part of the coverage and valuational differences between recorded exports and imports that is proportional to trade—fall from 7 per cent for annual data to 2 per cent as calculated from monthly data. That this estimate decreases, along with that of the transport lag, is precisely consistent with the collinearity argument, since the relevant coefficients enter the equation with opposite signs. This overstates the change in â, however, because the two estimates are not strictly comparable. It is not possible to exclude such asymmetrically recorded flows as trade with the Sino–Soviet area and special category trade from the monthly series, whereas it is possible with respect to the annual data; consequently, additional discrepancies in coverage enter the monthly equation. Recorded net exports of the world to the Sino–Soviet area have amounted to about ½ of 1 per cent of global exports in recent years, and net exports of special category trade, a full percentage point. Thus, the decrease in a defined consistently is perhaps no more than from 7 per cent to 3½ per cent.

Moreover, the estimate of k—the part of the discrepancy in coverage that is not proportional to trade—increases from about $½ billion in the annual–data results to $6½ billion in the monthly–data results (expressed at an annual rate). This change amounts to about 3 per cent of world exports, valued at mid– sample. Alternatively’, the equation can be re-estimated with k constrained to equal zero. In this case, the estimate of a increases by 1½ percentage points; compare lines 1 and 2 of Table 5. (On economic grounds, there does not seem to be any a priori reason for constraining valuational and coverage discrepancies to be proportional, however, and the Durbin–Watson statistic is reduced.) For both of these reasons, the 2 per cent estimate of a is not simply the difference between freight and insurance and global net underreporting of imports.

Table 5.

Regression Estimates of the Transport Lag Equation for World Trade, Using Alternative Specifications, Definitions, or Samples, Based on Monthly Data1

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See footnotes to Tables 1 and 2.

The proportion of trade invoiced in U. S. dollars is assumed to undergo a once–for–all change beginning in January 1974.

In this regression, the effective exchange rate for the U. S. dollar presented in IFS has been substituted for the trade–weighted moving average that was constructed for this study.

In the light of these comments, the monthly estimate of a does not seem to be implausibly low. Nevertheless, a respectable argument for negative bias in this estimate does exist. If the transport lag has decreased during the sample period—say, because an increasing proportion of trade is transported by aircraft—then all the ci can be shown to be subject to some degree of negative bias. (The demonstration is by application of the common result on omitted variables.) The effect on the estimate of the transport lag is diluted, if not negated, because the bs are functions of ratios of the cs, but the effect on a is definitely negative. To investigate this possibility, the monthly model was re-estimated with data from the latter half of the sample, 1967–75. The results, given in line 3 of Table 5, do not indicate an increase in a, but rather a slight decrease (compare line 1). The hypothesis is not conclusively disproved, as the estimate of a becomes less stable in the smaller sample (the t–value being half as large), suggesting a complex assortment of factors bearing on this coefficient in recent years. But it is quite unlikely that there exists a downward trend in the transport lag sufficiently strong to invalidate the general magnitudes of the reported estimates.

A second source of difference between yearly and monthly estimates arises because the monthly sample includes an additional year–1975. If the annual samples are similarly extended through 1975, the corresponding estimate of b is decreased considerably, bringing it closer to the reported monthly results. Further experimentation reveals, however, that while both estimates decrease somewhat when 1975 is added to the sample (first and fourth lines of Table 5), there remains a substantial difference between them.

A third difference is that the estimate of the transport lag based on annual data reflects the magnitude specific to years ending in December. This may be important in the light of the common assumption that revisions to trade data that cannot be allocated to particular months are added by statistical agencies to the December figure—trade that will not give rise to corresponding import flows, lagged or unlagged. The transport lag equations were modified to allow a constant percentage of December trade to be excluded from the normal pattern of recorded imports, but the econometric results were ambiguous. The estimate of the “December factor” was very sensitive to the omission of the final year or two from the sample (in addition to those very recent years, the numbers for which are still subject to revision). Either the data do not strongly support the hypothesis of proportionate December revisions or there has been a recent change in the pattern. 24 Consequently, the factor has been omitted from the equations reported here. (The modified specifications and corresponding empirical results are given in Section F of the Supplementary Notes mentioned in footnote 6.)

To the extent that world trade is not denominated in U.S. dollars, a change in the effective dollar rate during the transport interval will affect the difference between exporter and importer records, as discussed in Section II. The monthly regression results suggest that, on average, about one half of world trade was invoiced in currencies other than the U.S. dollar during the years 1959–75. This is not out of line with the findings of Grass– man and Magee. (Those studies reported that about two thirds of the examined trade flows were denominated in the exporter’s currency and one fourth in the importer’s currency—less in either case if the United States was the partner—for a small and recent sample of highly industrialized countries.) 25

Magee argues, quite reasonably, that these proportions will tend to vary with the strength or weakness of the dollar. A crude preliminary test of this hypothesis can be made by allowing the coefficient on the exchange rate variable to shift. Estimates are shown in line (5) of Table 5 for a dummy variable that takes the value of unity in January 1974 and later months, zero in preceding months. The results have the expected sign and are of reasonable magnitudes: an average of one fourth of world trade was invoiced in currencies other than the dollar through 1973 but a much higher proportion, about three fourths, in the succeeding portion of the sample. Neither aspect of the exchange rate effect approaches statistical significance, however, and therefore this specification was not used to calculate the preferred results (Table 1). Changing the period of the hypothesized shift in invoicing practices does not much affect the numerical results if the shift occurs later, but the estimates become unreasonable (although insignificant) if the change is specified to commence earlier—say, 1971 or 1972. This suggests that the non–dollar invoicing is more recent than the devaluations of 1971 and 1973, as would be expected if the adjustment of institutional arrangements occurs with a lag. If this interpretation is correct, the accumulation of additional observations will tend to add precision and statistical significance to these preliminary results.

In a forecasting application, the transport lag equation yields estimates of the timing asymmetry for the forecast period based on projections of world export values and an effective exchange rate for the U.S. dollar. Regarding the exchange rate variable, a convenient simplification of the preceding empirical treatment may be employed. The potential exchange rate effect was defined initially in terms of a flow between two particular regions, the exchange rates included in the weighted average being those of the countries in the exporting region and the weights reflecting exporters’ shares in the importing region. (See the Statistical Appendix.) Such an elaborate variable would be cumbersome to use in an actual forecasting exercise, and the regional disaggregation has been dropped in any case. The effective exchange rate for the U.S. dollar published in IFS was tried as a proxy and found to be a nearly perfect substitute. The value of d is slightly different, but all other coefficients and related regression statistics are virtually unchanged. This is shown in Table 5, the first and final entries (the basic equation including the exchange rate effect and the “forecasting version” of that equation, respectively). 26 The timing–asymmetry estimates for the years 1967–77 presented in Table 1 are based on this forecasting version of the equation. For a decomposition of the asymmetry into components attributable to the lag itself and to the exchange rate effect, and a side calculation on the size of the effect of the hypothesized shift in dollar invoicing, see Section G of the Supplementary Notes mentioned in footnote 6.

V. Conclusions

The central finding of the present study relates to the length of the transport lag implicit in recorded world trade. In terms of flows, about 3 per cent of exports is not received and counted as imports until the following calendar year. In terms of time units, the transport lag averages about 0.6 month (if the assumed intramonth distribution of trade is not wide of the mark). The global timing asymmetry attributable to the transport lag varied between zero and $6½ billion during the 1970s. For forecasting purposes, the asymmetry on world merchandise account that remains after taking account of the timing asymmetry is relatively smooth.

Empirical research on the transport lag is constrained by the availability of data in that it is possible to improve accuracy by estimating components of the lag distribution over relatively short units of time, or by estimating the lag for relatively small groups of countries, but not by both. The former alternative is more fruitful by far. Essentially, the lesser degree of collinearity among the relevant monthly series permits satisfactory discrimination between the lag and other effects, whereas geographic disaggregation with annual data appears to compound this problem severely. Regressions with monthly data indicate that the lag distribution extends over four periods, with most of the weight on the unlagged term. The alleged tendency for statistical authorities to include unallocable revisions in the December trade figures does not receive consistently strong empirical support.

Recorded “world” imports (using the IFS definition) tend to exceed “world” exports by about $6½ billion a year plus 2 per cent, after allowing for the transport lag. At present, the $6½ billion amounts to about an additional ½ of 1 per cent—implying, say, that import values exceed exports by 3 per cent apart from timing. (As a percentage of trade, the timing asymmetry is small, ⅓ of 1 per cent if trade is growing at the rate of 10 per cent a year, and so on.) Reflected in the 3 per cent are two important instances of incomplete partner records—the flow of net exports to the Sino–Soviet area, roughly ½ of 1 per cent of world trade in IFS, and net exports of special category commodities, 1 per cent. Adjustment for these recording inconsistencies would thus bring import values to a level roughly 4½ per cent greater than recorded exports on average (again, adjusting for the transport lag). The remaining nonreporting countries are believed to be net exporters, taken as a group, but in amounts substantially less than ½ of 1 per cent of recorded world trade. At 4½ per cent, the excess of recorded import values over export values is consistent with the conjecture of general net underreporting of imports, unless freight and insurance are much smaller in proportion to f.o.b. values than is commonly supposed.

Grassman and Magee, in published studies, report evidence that international trade is not denominated predominantly in U.S. dollars. To the extent that it is not, there is a tendency for recorded import values to exceed (fall short of) exports if the dollar depreciates (appreciates) during the transport interval. With allowance for this effect in the transport lag equation, the proportion of trade not invoiced in U.S. dollars is estimated to be on the order of 50 per cent. While this estimate is subject to a large margin of error, it does tend to confirm—on a very broad if indirect basis—the findings of Grassman and Magee, which were necessarily based on quite narrow samples. There is also evidence, although even less certain, that the proportion of non– dollar invoicing has increased in recent years, indicating a somewhat reduced role for the U.S. dollar as a vehicle currency.


The annual time series for bilateral export and import flows among regions are from the IMF Direction of Trade data bank. In these series, trade with nonreporting countries, notably the Sino–Soviet group, is excluded both in reporter and in partner records. Special category trade and trade with “countries not specified” are necessarily excluded from regional flows. The latter, but not the former, is included in global totals; importer records of special category trade are relatively incomplete. Data from national sources have been substituted for the DOT partner entries for Malaysia and Singapore for the years 1958–66. The monthly time series for global exports and imports are from the IMF International Financial Statistics data bank. Exports to and imports from nonreporters are included.

The effective U. S. dollar exchange rates calculated for this study are weighted averages of the period–average dollar exchange rates (inverse of line rf in IFS) of the countries in the exporting region (those having exports valued at $0.5 billion or greater in 1975). The weights are the shares of the exporting countries in that region’s total exports to the importing region. The weights vary over time, being linear interpolations of the shares at the beginning and end of the sample period, 1959–60 and 1974–75, respectively. For the “forecasting version” of the monthly equation, the effective exchange rate given in IFS (line amx on the page for the United States) was substituted for the world weighted–average rate just described.


Mr. Hemphill, economist in the Current Studies Division of the Research Department when this study was prepared, is now in the European Department. He is a graduate of Monmouth College (Illinois) and Princeton University.

The author is indebted to colleagues in the Fund for unusually generous interest in, and correspondingly numerous comments on, earlier drafts. The result remains the responsibility of the author.


The asymmetry is similar to the central bank “float” in that both arise because of a transit delay. However, the float refers to a stock of items while the asymmetry is a flow—in effect, the change in the “international trade float” over a specified period.

A standard reference on this topic is John S. Smith, “Asymmetries and Errors in Reported Balance of Payments Statistics,” Staff Papers, Vol. 14 (July 1967), pp. 211–36; see especially p. 223. Smith explains that the lag would not arise if trade data were collected on a balance of payments basis, according to which a shipment is counted as exports by one partner and as imports by the other at the moment when ownership changes. However, in practice, trade data are generally collected as goods move through customs, and the information required for adjusting more than a few unusual shipments to the balance of payments basis is not available.

For an earlier description of the problem, see Herbert B. Woolley, “On the Elaboration of a System of International Transaction Accounts,” Ch. 3 in Problems in the International Comparison of Economic Accounts: Studies in Income and Wealth, Vol. 20, National Bureau of Economic Research (Princeton University Press, 1957), pp. 217–90, especially p. 263. Also, it is noted regularly in the introductory notes contained in International Monetary Fund, Direction of Trade Yearbook, various issues.


See, for example, Organization for Economic Cooperation and Development, OECD Economic Outlook, No. 23 (July 1978), Table 27 and the discussion on pp. 42–43 and 117.


The residual asymmetry in recent years is smaller and shows a slightly different movement if the trade balances of countries that are not members of the Fund, other than Switzerland and Hong Kong, are taken into account (that is, if “world” trade is defined on a truly global basis); see the final column of Table 1. Of course, increased lumpiness of any component of the residual asymmetry, such as Soviet agricultural imports, would reduce the prospective sufficiency of the timing asymmetry as an explanation of the irregular part of the total.


See Sven Grassman, “A Fundamental Symmetry in International Payment Patterns,” Journal of International Economics, Vol. 3 (May 1973), pp. 105–16, and Stephen P. Magee, “U. S. Import Prices in the Currency–Contract Period,” Brookings Papers on Economic Activity: 1 (1974), pp. 117–68.


These estimates can be shown to be the same as those resulting from nonlinear least–squares estimation and therefore asymptotically unbiased and efficient. See Jan Kmenta, Elements of Econometrics (New York, 1971), pp. 442-45. The nonlinear estimation algorithm used in this paper was provided by Data Resources, Inc.


For the case in which freight costs are assumed to vary with the transit lag, see Section A of a set of Supplementary Notes, which is available upon request from the author, in care of the European Department, International Monetary Fund, Washington, D. C. 20431.


In a foregoing passage, it was argued that shipments exported and imported in the same month are subject to a lag of, roughly, 0.25 month on average, shipments exported and imported in successive months to an average lag of 1.25 months, and so on see the discussion on expressing the transport lag in units of time. This logic has been carried over to the computation of the exchange rate change series: ri* is a weighted average of the percentage changes over i and (1 + i) months, with weights of 0.75 and 0.25, respectively. While logical consistency is thus preserved, the empirical results are not noticeably affected by this a priori specification—relative to, say, a straightforward i–period percentage change.


For additional notes on data sources, see the Statistical Appendix.


These regional designations are the ones utilized in DOT and in IFS, through 1979, “more developed primary producing countries” being the combination of “other Europe,” Australia, New Zealand, and South Africa. Trade with the so–called Sino–Soviet area countries and with other countries that are nonreporters is omitted.


The disaggregation may be carried further. Paijit Habanananda has studied selected bilateral flows between individual countries of different regions; see “The Transit Lag in Trade Statistics,” Papers on International Financial Statistics (International Monetary Fund, January 22, 1979).


For a description of the method used in preparing the estimates of bias, see Section B of the Supplementary Notes mentioned in footnote 6.


Let s be the ratio of the specified end–year months’ (December plus November plus …) exports to annual exports, estimated by taking the arithmetic mean over the sample period. Then, b^y=s^b^; see part (c) of Table 2.


To the extent that the excluded shipments are correlated with the included ones—which is probably large in this case—the estimated timing asymmetry figures will not be biased, despite the upward bias in the regression estimate of b.


For regions’ exports to the “world,” the fourth–quarter flow was estimated by applying the relevant proportion calculated from IFS monthly data to the annual DOT figure.


A mixture of correct and incorrect signs, with instances of statistical significance being distributed fairly evenly between the two categories, is typical of the estimates of d based on annual data—irrespective of changes in, for example, sample length, explanatory variables, or geographic disaggregation. Additional regression results for equation (8), including the exchange rate effect, are presented in Section C of the Supplementary Notes mentioned in footnote 6.


It may be objected that, in general, standard errors of additional lag terms can be large because of collinearity, in which case application of the t–test will result in inappropriate exclusion of those terms and a downward–biased estimate of the average lag. In the present instance, however, the sign on the first excluded term is negative, and inclusion of additional terms does not result in a larger average lag. Moreover, bias from this source in the estimate of the lag measured in units of time does not imply bias in the estimated asymmetry values, since if the terms are collinear, the included terms capture the effects of the excluded ones. It has been pointed out to the author that the equation can be rewritten so that the lag terms are all first differences, a modification certain to lessen the degree of collinearity among the regressors. However, when the equation modified in this way was fitted, the estimates of the bi remained unaffected to two (in most cases, three) significant digits, even in the specification including six lag terms (corresponding to the last line of part (a) of Table 4). Thus, the problem of collinearity among terms of the form (Xt – Xt-i) is minimal in the present context.


Apart from the possibility of sampling error, this counterintuitive pattern may be due to customs verification procedures. Declarations containing irregular or implausible information may be set aside until further checking is possible, the shipments involved being counted as imports when this process has been completed.


Other things being equal, attribution of part of the value of imports to exchange rate change increases the remaining difference between exporter and importer records if dollar depreciation has been more common than dollar appreciation. This larger difference, in turn, results in generally smaller reduced form coefficients—a reduction in â, but an indeterminate effect on the b^i.


For a brief discussion of the econometric factors that account for differences in lag estimates from data of different frequencies, see Section E of the Supplementary Notes mentioned in footnote 6.


The simple correlation coefficient between monthly values of X and ΔX is even smaller, 0.21, but this is not the appropriate statistic for comparison, since the monthly version of the model contains three terms of the form Xt-Xt-i. The quoted statistic, 0.35, is the correlation coefficient, r, resulting from regressing X on all terms of the form Xt-Xt-i, just as the 0.97 for annual data could be calculated by regressing X on ΔX.


For example, see Smith (cited in footnote 1), pp. 223–24.


These averages naturally mask commodity differences; for example, for Japan, the range is from 2 days for electronic calculators (the median lag for calculators is zero days, as just over one half are shipped by air) to 52 days for steel plates and sheets.


Magee gives a figure of 31 days for the average entry lag for the Federal Republic of Germany (Table 4, p. 133), but this is clearly a typographical error, as none of the components of the mean approach this figure. The correct value, which is 15 days, can be computed from the horizontal sum in his table.


As discussed, the revision pattern observable in published time series indicates that estimation would be impaired by including data from 1976 and 1977 in the sample, but there is no evidence that earlier years are likely to be affected by outstanding revisions. The Fund’s Bureau of Statistics reports no change in its collecting or processing procedures dating from 1974 or 1975—such as the cutoff date for incorporating late revisions—that would explain the apparent tapering of the December factor.


See Magee, pp. 118–19, and Grassman (cited in footnote 4), passim.


The exchange rate variable was transformed by computing percentage changes. In the forecasting version, the value zero was used for all months through December 1970 because the U. S. effective rate has not been calculated for earlier periods in the IMF Data Fund.