Do Unit Value Export, Import, and Terms-of-Trade Indices Misrepresent Price Indices?
Author: Mick Silver

Unit value export and import indices compiled from returns to customs authorities are often used as surrogates for price indices in the analysis of inflation transmission, terms of trade (effects), and to deflate import and export value series to derive volume series. Their widespread use is mainly due to their low cost relative to establishment price surveys. This paper provides evidence of substantial errors and bias in their representation of such price changes. Their continued use would mislead economic analysis. The paper considers the efficacy of alternative strategies for their improvement, and argues for a move to establishment-based price surveys.


Unit value export and import indices compiled from returns to customs authorities are often used as surrogates for price indices in the analysis of inflation transmission, terms of trade (effects), and to deflate import and export value series to derive volume series. Their widespread use is mainly due to their low cost relative to establishment price surveys. This paper provides evidence of substantial errors and bias in their representation of such price changes. Their continued use would mislead economic analysis. The paper considers the efficacy of alternative strategies for their improvement, and argues for a move to establishment-based price surveys.

Export and import unit value indices (UVIs) are based on data from customs documentation and are so named because they take as their building blocks, for individual commodity groups, the ratio of the unit value in the current to the reference period. They measure, for individual commodity groups, the change over time in the total value of shipments divided by the corresponding total quantity. These elementary-level unit value ratios—also, and hereafter, referred to as (elementary) UVIs—are subsequently aggregated across commodity groups using standard weighted index number formulas where the weights are the relative shares of the commodity group in total exports/imports. Export and import price indices (PIs) have as their building blocks, at the elementary level, the price change of well-defined representative items derived from establishment surveys. Export and import UVIs by necessity differ from PIs because of their source data.

This paper considers whether export and import UVIs derived from customs data, and commonly used as surrogates for export and import PIs, represent or misrepresent such price changes. UVIs as measures of price changes of imported and exported goods serve economic analysis in many important ways. They are used as short-term indicators of inflation transmission, to measure changes in a country’s terms of trade (ToT) (effect), and as deflators of export and import values to yield measures of changes in export and import volumes. Yet, in spite of their widespread use they are subject to well-recognized errors and bias.1 The issue of concern is whether such bias misleads economists in their economic analysis to the extent that their compilation and use should not be recommended. Also of importance is to consider what might be done by statistical agencies if UVIs are found wanting.

Bias in UVIs is mainly attributed to changes in the mix of the heterogeneous items recorded in customs documents, but may also arise from the poor quality of recorded data on quantities. The former is particularly important given the increasing differentiation of products and turnover of differentiated products that is a feature of modern markets. UVIs may suffer further due to an increasing irrelevance of the source data with first, increasing proportions of trade being in services and by e-commerce, and hence not covered by customs data, and second, a constraint on the coverage of such data for countries in customs and monetary unions, for which intra-union trade date may no longer be regularly collected.

Few deny, including United Nations (1981),2 that narrow specification PIs provide the best measures of relative price change and that, a priori, there are potentially significant biases in using customs unit values to measure price developments in international goods trade. Yet, unit value proxies for narrow specification price data collected from establishments are still used because they are by-products of existing customs administration systems and have relatively low incremental cost compared with the price surveys of establishments needed for narrow specification prices.

The concern over bias in UVIs is not new. Early critical studies of unit value bias as measures of import and export price changes and ToT include Kravis and Lipsey (1971 and 1985). The United States discontinued publication of unit value trade indices in 1989 due to the concern over bias and introduced trade PIs based on establishment surveys. A move away from UVIs based on customs documentation has also been prompted by the introduction of a customs union for the euro area.3

I. UVIs and Their Bias

This section first outlines the nature of the bias in a unit value index (UVI) arising from changes in the compositional product mix, then considers it more formally by means of the properties of the UVI in relation to the main axiomatic tests used in index number theory to justify formulas, and finally in relation to economic theory.

A UVI, PU, for commodity group i, for period 1 relative to a reference period 0 is given for comparison over m = 1, …, M prices, Pm1, and quantities, qm1, in period 1 and over n = 1, …, N prices, pno, and quantities, qno, in period 0, where m∊i and n∊i, by


Higher level indices aggregate PU,i over the i commodity groups using standard index number formulas such as Laspeyres and Fisher indices (ILO and others, 2004a, Chapter 15).

Unit Value Bias Illustrated

Consider, for example, trade in refrigerators. With the exception of the ‘‘size’’ of the refrigerator, assume the mix of all price-determining characteristics remains constant over the periods compared, or is proxied by ‘‘size.’’ Assume further that there is a meaningful division of ‘‘size’’ into the three groups of ‘‘small,’’ ‘‘medium,’’ and ‘‘large,’’ and a change in purchasing patterns toward smaller refrigerators. In an illustrative example below, adapted from United Nations (1981, p. 15), refrigerator prices, p, double for each size group and there is a shift to the quantities, q, sold now, in proportion to 2, 3, and 5 going from largest to smallest, from what was then 5, 3, 2, although total quantity remains the same over time. The value, v, is given as p × q.

As prices in each size group have doubled, a weighted average of these price changes, Σiwi(piNow/piThan), over the i size groups is 2.0. But the change in the unit value is 3.4/2.3 = 1.478. There is a downward bias in the UVI due to the change in the product mix toward cheaper refrigerators.

article image

UVIs: The Test Approach

The test or axiomatic approach to index number formula choice is well established and is used with regard to elementary index numbers in ILO and others (2004a, Chapter 20). If the items whose prices are being aggregated are identical—that is, perfectly homogeneous—a UVI has desirable properties. Consider the case where the exact same item is sold at different prices during the same period, say lower sales and higher prices in the first week of the month and higher sales and lower prices in the last week of the month. The unit value for the monthly index solves the time aggregation problem and appropriately gives more weight to the lower prices than the higher ones in the aggregate. If the elementary UVI in Equation (1) is used as a price index (PI) to deflate a corresponding change in the value, the result is a change in total quantity which is intuitively appropriate, that is


Note that the summation of quantities in the top and bottom of the right-hand side of Equation (2) must be of the exact same items for the expression to make sense.

Heterogeneous items

The very nature of an index number problem is that the desired measure is the change in price or volume of an aggregate over different items, or items of different qualities. It is well established in index number theory that the superlative class of index number formula, which includes the Fisher, Törnqvist, and Walsh index number formulas, are appropriate (ILO and others, 2004a, Chapters 15–8). The component product groups of UVIs derived from customs data cannot a priori be assumed to aggregate over homogeneous items.

  • The UVI fails the Proportionality Test: P(p, λp, q0, q1) = λ for λ > 0; that is, if all prices are multiplied by the positive number λ, then the new PI is λ. The UVI only satisfies the proportionality test in the unlikely event that relative quantities do not change.

  • It follows from the failure of the proportionality test that the UVI also fails the Identity or Constant Prices Test: P(p,p, q0, q1) = 1; that is, if the price of every good is identical during the two periods, then the PI should equal unity, no matter what the quantity vectors are. It only satisfies the identity test if relative quantities—that is, the composition of the products compared—do not change.

  • The UVI, however, satisfies the proportionality in current period prices test, P(p0, λp1, q0, q1) = λP(p0, p1, q0, q1) for λ > 0; that is, if all period 1 prices are multiplied by the positive number λ, then the new PI is λ times the old PI.

  • The UVI fails the Invariance to Changes in the Units of Measurement (commensurability) Test: p(α1p10,,αnpn0;α1p11,,αnpn1;α1-1q10,,αn-1qn0;α1-1q11,,αn-1qn1)=p(p10,,pn0;p11,,pn1;q10,,qn0;q11,,q11) for all …1 > 0, …, αn > 0; that is, the PI does not change if the units of measurement for each product are changed. For example, if the measurement of one of the products changed from pounds weight to kilograms, the index should not change.

UVIs pass the other main index number tests, including the time reversal test, the circularity test, and the product test. However, that it is affected by changes in the composition of products, and (changes in) its units of measurement—that is, it fails the proportionality and commensurability tests—is critical to conclude that it is an inappropriate measure.

That a PI can be affected by changes in relative quantities is a serious deficiency. The essence of the fixed basket concept of PIs is the need to hold quantities constant over time. There is a very real sense in which a UVI should not be properly described as a PI unless applied to transactions for homogeneous products and thus, by definition, the composition of products cannot change.

A particular instance of the effect of the failure in the commensurability test impacting adversely on the UVI is one in which the quality of products imported/exported changes. When this occurs, the actual units of measurement may not change, but the implicit unit of productive service or utility would change, and bias the index. Accounting for the effects of quality changes on prices is difficult enough for index number work based on price surveys (ILO and others, 2004a). Customs data on quality characteristics are likely to fall well short of the corresponding information that would normally be available from establishments producing for export, or purchasing as imports.

Balk (1998) compares UVIs with a Fisher “ideal” index (though see also Silver (2008)), and draws the following conclusion: the unit value bias will be equal to zero for a comparison between periods 0 and 1 if one or more of the following conditions are met:

  • All base period prices pm0 are equal to each other and all current period 1 prices pn1 are equal to each other.

  • All quantity relatives qm1/qm0 are equal to each other.

  • There is no correlation between pm0 and qm1/qm0, and also no correlation between pn1 and qm1/qm0.

These are all highly restrictive conditions. The first condition defeats the purpose of a PI, in that if all prices were equal in each period, then the price change of a single product would suffice. The second condition is the assumption required above for satisfaction of the identity and proportionality tests. If all quantity relatives were equal, and this were known, the PI number problem would be solved by dividing the total outlays by this single quantity relative. The third condition arises from the fact that if price relatives and quantity relatives are uncorrelated, then a change in prices would not affect quantity relatives and vice versa, and there will be no change in the composition mix due to relative price changes. There may be some markets in which there is market failure or temporal inconsistencies, but for the large part the laws of economics cannot be assumed away.

UVIs: Economic Theoretic Approach

Bradley (2005) takes a cost-of-living index defined in economic theory4 and compares the bias that results from using unit values as “plug-ins” for prices. Bradley (2005) finds that if there is no price dispersion in either the current or reference period compared, the unit value (plug-in) index will not be biased against the theoretical index. But this is equivalent to the case of a single item and the index number problem arises because we are aggregating across more than one item. He also finds that if there is price dispersion in the current period but not the reference period, a unit value “plug-in” would have a downward bias; if prices are dispersed in the reference period but not in the current period, there will be an upward bias in the index; and if there is price dispersion in both periods, there is a guarantee (there is a zero probability that the condition of no bias will hold for any arbitrary data generating process) that there will be a bias in the “plug-in” UVI, but one cannot sign that bias.

UVIs: The Cause for Concern

UVIs derived from data collected by customs authorities are mainly used by some countries as surrogates for price changes at the elementary level of aggregation. The following are the grounds upon which UVIs can be deemed unreliable:

  • Bias arises from compositional changes in the quantity and quality mix of what is exported and imported. Even with best practice stratification, the scope for reducing such bias is limited due to the sparse variable list—class of (quantity) size of the order and country of origin/destination—available on customs documents. Indeed, Párniczky (1974) shows that it does not follow that such breakdowns are always beneficial to a UVI.

  • For unique and complex goods, model pricing can be used in establishment-based surveys where the respondent is asked to price each period a product, say a machine with fixed specified characteristics. This possibility is not open to UVIs.

  • Methods for appropriately dealing with quality change,5 temporarily missing values, and seasonal goods can be employed with establishment-based surveys to an extent that is not possible with UVIs.

  • The information on quantities in customs returns, and the related matter of choice of units in which the quantities are measured, has been found in practice to be seriously problematic.

  • With customs unions, countries may simply have limited intra-area trade data to use.

  • An increasing proportion of trade is in services and by e-trade, and not subject to customs documentation.

  • UVIs rely to a large extent on outlier detection and deletion. Given the stickiness of many price changes, such deletions run the risk of missing the large price catch-ups when they take place and understating inflation.

  • Valuation requirements for the deflation of the aggregates of the 2008 System of National Accounts (2008 SNA)6 are determined for UVIs by customs procedures that are not in accord with the accrual principle of the 2008 SNA (see Chapter 3, paragraphs 3.161-5).

A main advantage of the use of UVIs is held to be their coverage and relatively low resource cost. However, the unit values used are drawn as nonrandom samples and exclude products traded irregularly; that have no quantity reported (especially for parts and machinery); have low-value shipments; and erratic month-to-month changes. The extent of such exclusions is substantial, as illustrated later in this paper. Establishment-based surveys can be quite representative. Often a small number of wholesalers or establishments are responsible for much of the total value of imports or exports and, assuming cooperation, will be a cost-effective source of reliable data. Further, good sampling, can, by definition, realize accurate price change measures and finally, the value shares of exports and imports, obtained from customs data, will form the basis of information for weights for establishment-based surveys.

II. Evidence

We adopt for brevity the terminology of PI to refer to an establishment-survey-based PI as distinguished from a customs data-based unit value index, UVI. The evidence is presented here first at the aggregate level. Results at a more disaggregated level are then considered. Given the above reasons to expect that UVIs will not be suitable surrogates for PIs, it is necessary to consider the empirical evidence available on the nature and extent of any differences. The evidence is presented in this section first at the aggregate level for some existing studies and then for Germany and Japan as new results. Results at a more disaggregated level will be considered later in the section for Germany and some other European countries.

Some Existing Studies

Angermann (1980) compared PI number changes with unit value changes for exports from and imports to the Federal Republic of Germany. Between 1970 and 1976, the (Paasche-ized, to be consistent with the UVI) PI for exports increased by 38.6 percent compared with 34.3 percent measured by (Paasche) UVIs. The discrepancy between such import PIs and UVIs was greater, at 45.8 and 33.1 percent, respectively. He also found that when UVIs were used to calculate the ToT effect there was a gain in 1976 of 1.4 billion deutsche marks to real income, at 1970 prices, compared with a loss of 6.6 billion deutsche marks when using a Paasche-ized PI.

Alterman (1991) compared price changes between March 1985 and June 1989 for the United States as measured by UVIs and PI based on establishment surveys that replaced them. For imports, over this period, the PI increased by 20.8 percent and the UVI increased by 13.7 percent. For exports, the figures were much closer, 13.0 and 12.2 percent for the PI and UVI, respectively. Some of the difference between the two series may be attributed to their use of different periods for weights. However, when PIs were recalculated using the same weights as the UVIs, the differences were exacerbated: a 20.6 and 16.4 percent increase for the import and export PIs, respectively. The average (absolute quarter-on-quarter) UVI change for imports and exports, respectively, were 27 and 70 percent greater than the corresponding PI changes. One method of considering whether such differences matter is to evaluate the implications of such discrepancies for deflation of the foreign trade component of the national accounts. Alterman (1991) found that the annualized second-quarter 1989 “real” trade deficit in March 1985 dollars would have been $128.4 billion if deflated by a UVI, but just $98.8 billion, 23 percent less, if deflated by a PI.

A review in 1992 of the unit value methodology used by the United Kingdom for its trade PIs led to their change in May 1996 to trade PIs, following similar changes in methodology by the United States, Japan, and Germany (Ruffles and Williamson, 1997). The annual averages of export prices in 1995 compared with 1994 increased by 6.6 percent using PIs compared with 8.1 percent using UVIs.

Such findings are not new. Kravis and Lipsey (1971) found that the prices of manufactured goods exported by developed countries to developing countries had risen over about 20 years by 75 percent, as compared with the 14 percent of the shown by UVIs. Kravis and Lipsey (1985) found a decrease in the ToT of manufactures relative to all primary products between 1953 and 1976 of over 36 percent, using PIs, almost a quarter greater than that suggested by the UVIs (28 percent). With a further correction for quality change, the price data suggested a fall in manufactures ToT of over 45 percent, more than 50 percent greater than UVIs.

Comparison of UVIs and PIs for Germany and Japan

This study compares UVIs and PIs for both Germany and Japan for exports and imports using monthly data for 1996:7-2006:9 from the IMF’s International Financial Statistics (IFS). Results are presented to ascertain the magnitude of the discrepancies between UVIs and PIs for measures of export and imports price changes as short-run indicators (month-on-month and month-on-12-month comparisons); long-run cointegration; and predictive ability (leading indicators). Export and import UVIs are also used for the measurement of changes in ToT and discrepancies between UVIs and PIs used for this purpose are also considered, as is the use of UVIs for the measurement of the ToT effect and as a long-run deflator.

Short-run indicator

Figure 1 compares month-on-month changes between UVIs and PIs for exports for Germany and identifies substantial volatility for UVIs. Silver (2007), upon which this paper is based, includes similar figures for exports and imports in both countries finding substantial discrepancies between PIs and UVIs. Although, for Japan in some periods, especially the earlier years, UVIs and PIs appear to track each other, this cannot be relied upon and breaks down in later periods.

Figure 1.
Figure 1.

Export Unit Value and Price Indices for Germany

Citation: IMF Staff Papers 2009, 002; 10.5089/9781589067950.024.A003

Table 1 provides summary statistics on the magnitude of the (absolute value of the) discrepancies: the ratio of UVIs to PIs for exports and imports in both countries along with the root mean squared deviation between the UVIs and PIs. The mean month-on-month discrepancy is calculated as ΣtT=2[|((UVIt/UVIt-1)/(PIt/PIt-1))-1|]/(T-1) (where || denotes the modulus—absolute value) and other summary measures are defined accordingly.7 The mean discrepancy for imports to Germany was 1.1 percent. A need exists to draw a line as to the extent to which a discrepancy is acceptable, in the sense that on empirical grounds the matter of choice between a UVI and PI is of little consequence. A discrepancy of 0.011 implies that if the month-on-month change in the PI was unity, no change, then the UVI would take a value of a 1.1 percent change on average; or if the PI was a 1 percent change, the UVI would be 1.01 × 1.011 = 1.021, a 2.1 percent change. Such discrepancies can be regarded as seriously misleading for economists. The discrepancy for individual months can of course be much larger than this mean, as reflected by the standard deviation of 1.0 percent and maximum of 7.3 percent points for these month-on-month changes. The month-on-12-month changes benefit from some positive and negative discrepancies over the 12 months compared canceling. Yet, with a mean 12-month PI change for German imports of 4.75 percent, a discrepancy of 1.8 percent on average and standard deviation of 1.6 percent (Table 1) provide no cause for complacency.

Table 1.

Average Discrepancy between Import Unit Value and Price Indices

article image

Summary measures of the absolute value of the discrepancy [(UV/PI)–1].

Such discrepancies might be argued to be a problem of magnitude rather than direction. Table 2 shows the extent to which positive (and negative) changes in UVI indices are mirrored by positive (and negative) ones in PIs. For about 25 percent of month-on-month comparisons, the signs differ; that is in one-quarter of comparisons the economist would read prices were rising (falling) when they were falling (rising). The results are better for month-on-12-month comparisons, but this cannot be relied upon, as German exports demonstrate.

Table 2.

UVI and PI: Percentage of Changes of Same and Different Sign

article image

Total excludes cases where either change is exactly unity.


It may be argued that the concern should be with the long-run equilibrium between the alternative measures and the extent of any short-run error correction. Unit root tests for Germany and Japan’s import and export UVIs, and corresponding PIs were conducted for month-on-month changes, month-on-12-month changes, and the index. The null hypothesis of a unit root was rejected at a 5 percent level for all month-on-month comparisons, and for all month-on-12-month comparisons, with the exception of German exports (for detailed results, see Silver, 2007). The UVIs and PIs were generally not I(1) and thus it was not possible to establish cointegrating relationships. Although it is the changes that are the concern of economic analysts, we considered the series themselves. The index series, not subject to differencing, were all I(1) and the cointegration test statistics all had p-values that exceeded 0.05; the null hypothesis of a unit root in the cointegrating regression could not be rejected at this level and we thus concluded at this level that the linear combination of the unit value and PI was not I(0), so they were not cointegrated.


A further question is whether UVIs have any information content useful to predict next month’s PI. Changes in the past UVIs may be used as indicators of future trade price changes. We estimated for each PI series: and tested the null hypothesis that β1j = 0 for all j and observed the sign if the null hypothesis was rejected (the signs were all positive when significant).


Table 3 shows the F-test for this null hypothesis to be rejected in three out four cases for the month-on-month indices and in all cases for month-on-12-month changes. Thus, for most cases UVIs have some predictive power in relation to PIs. However, when they have, it is of little substance. Table 3 provides the means of the PIs and standard errors of the regression. It can be seen that the predictive intervals are quite wide—for example, the 95 percent interval for German imports is +1.8 percent. Although lagged UVIs have some predictive power regarding PIs, there is the question as to whether lagged UVIs have any contribution to predictive power over and above that of lagged values of the PIs themselves—that the UVIs Granger-Cause the PIs; that lagged UVIs better predict the PIs than lagged PIs would themselves. The test requires ordinary least squares (OLS) (given the stationarity) estimates of and tests for the joint hypothesis that β1j = 0 and α2j = 0 for all j. The Granger-causality (GC) tests in Table 3 find that in half the cases lagged UVIs contain no predictive power over and above lagged PIs, but this is not to demonstrate that in the cases where there is some such power UVIs GC PIs, as the GC tests reject the null hypothesis that PIs GC UVIs.

Table 3.

Predictive Ability of UVIs in Relation to PIs

article image



The above evidence is that UVIs are misleading proxies for PIs: they mislead in the sense that the relative and absolute errors can be substantial and that in many cases the signs of changes are wrong. There is no evidence of long-run (cointegrating) relationships and UVIs are of little further help for predicting PIs.

ToT indices

The concern above was with bias in UVIs as indicators of import and export price inflation, as measured by PIs. Yet, another use of UVIs is in the measurement of changes in the ToT of a country, determined as the ratio of the PI of exports to the PI of imports. If export and import UVIs are used as surrogates for export and import PIs, and export and import UVIs are biased to the same extent and direction, the UVIs will provide a correct indication of changes in the ToT as the bias cancels. However, if the export and import UVIs are biased in different directions, then the ToT UVI bias will compound. Our analysis is similar to that used above, but for ToT measured using UVIs instead of PIs.

Table 4 shows the average discrepancy between the UVI and PI measures of ToT. The discrepancies are generally larger than the substantial discrepancies found in Table 1 for the export and import indices. For example, the mean month-on-month discrepancy for ToT changes for Germany was 1.3 percent compared with 1.1 and 0.9 percent, respectively, for imports and exports. For month-on-12-month changes, the ToT discrepancy for Japan was 3.7 percent compared with 2.4 and 2.5 percent for imports and exports, respectively. The ToT discrepancy for Japan implies that if the TOT PI change was unity, the ToT UVI would on average show a month-on-month change of 3.7 percent with, given its standard deviation over time of 10 percent (0.10) and maximum of 70 percent (0.70), the possibility of very misleading results.

Table 4.

Terms-of-Trade Indices: Discrepancy between UVIs and PIs

article image

Table 5 presents the results on the percentage of months in which ToT UVIs have the same sign to their change as ToT PIs. ToT indices perform worse on average than export and import indices, Table 2, in this respect. The month-on-month ToT indices had the wrong sign in over one-third of the month-on-month comparisons. Japan's month-on-12-month series had the wrong sign in 22 percent of cases, but the export and import series had the wrong sign in 15 and 4 percent, respectively (Table 2).

Table 5.

Terms of Trade: Percentage of Changes of Same and Different Sign

article image

Total excludes cases where either change is exactly unity.

In order to establish whether the ToT indices measured by UVIs and PIs were cointegrated as a first step, we undertook unit root tests finding that they did not have unit roots and thus are not cointegrated (for detailed results, see Silver, 2007). The ToT indices measured as lagged UVIs were found to have some predictive information in relation to ToT PIs but it was very weak, as demonstrated by the relatively large standard errors of the regression in relation to the means of the ToT, given in Silver (2007). In the case of Germany, lagged ToT UVIs had no predictive ability over ToT PIs, but in Japan, lagged UVIs had some such ability; PIs were found to have a similar predictive effect for UVIs, so we could not establish that ToT UVIs Granger-cause ToT PIs.

ToT effect

ToT effect, or trading gain (loss), is a measure of the effect on income of changes in the ToT of a country, the relative price change of imports against exports. The 2008 SNA (Chapter 15, Section D) outlines the method of calculation as


where the first term is a measure of the goods and services balance (exports of goods and services (X) less imports of goods and services (M)) using a single deflator, P, and the second term is the goods and services balance by taking the difference between a volume (say, constant price) measure of exports and a volume measure of imports, that is after X and M have been deflated by respective PIs for exports and imports, Px and PM. Note in the second term how, for example, as export prices increase more slowly than import prices, the larger the sum deducted from the first term is, and hence the smaller the ToT effect is. Note also that the magnitude of the ToT effect is contingent on the deflator in the first term. There is no agreement as to the best deflator to use for this component (Silver and Mahdavy, 1989). The interpretation of the trading gain would be in terms of the gain in purchasing power with regard to the bundle of such goods and services to which P relates.

Table 6 shows the annual ToT effects for Germany and Japan in each case measured in terms of the change in prices for the preceding year and in terms of the purchasing power of imports, P = PM, although a similar conclusion arises from using exports or some average of the two. Data are also provided for each year on the country’s trade balance. The effect of using UVIs to calculate the ToT effects as against PIs is most marked. Note how, for example, in 2005 Japan’s trade balance of 6,956 billion yen is eliminated by the adverse change in its ToT when using PIs, but only halved when using UVIs.

Table 6.

Terms-of-Trade Effect: Previous Year’s Prices

article image

National accounts estimates of exports minus imports of goods and services (IMF, International Financial Statistics).

Long-run changes and deflation

Table 7 is concerned with comparing long-run changes between UVIs and PIs. One way of considering this is in terms of the use of such indices as deflators. In Table 7, the values of exports and imports of Germany and Japan are deflated over the period from 1999 to 2005 by corresponding UVIs and PIs, and the results are compared. The volume of exports by Japan can be seen to have increased by 50 percent over this period when a UVI deflator is used, but the increase is halved when a PI is used. The volume of imports by Germany is about constant over this period when a UVI deflator is used, but fell by about 10 percent using a PI deflator.

Table 7.

Comparison of Deflated Exports and Imports by UVIs and PIs

article image

The evidence is that export and import UVIs are inadequate surrogates for their PI counterparts when used in economic analysis. Such analysis includes their use in the measurement of short-and long-run inflation, prediction, ToT, ToT effects, and as deflators. Indeed, the evidence is that they are seriously misleading.

III. What Is to Be Done?

Given what should be grave concern over the use of UVIs, there is the practical matter of what should be done. UVIs are used by most countries and a move to PIs has resource consequences.

One possibility is to identify whether there are particular products less prone to UV bias and utilize UVIs for these subaggregates in a hybrid overall index. This has the resource advantage of undertaking price surveys only for products for which they are necessary. The efficacy of such advice depends on the extent to which reliable UVIs will be available at a disaggregated level.

Use Unit Value Subindices for Homogeneous Product Groups: The Reliability of Subindices

Disaggregated export and import UVIs and PIs for Germany

We extend the study to disaggregated monthly data for Germany. Such data are for export and import UVIs and PIs for the period from January 2000 to November 2006 and cover 150 series for which comparable data are available at the four-digit level of the Statistical Classification of Products by Activity in the European Economic Community, 2002 version (CPA). They are Paasche index numbers whose elementary aggregate building blocks are UVIs as opposed to PIs.

The results in Table 8 are for the 15 series that have the least difference between the PI and UVI series. The results for these “best” groups have an average discrepancy and volatility in excess of that for the weighted aggregate import PI found for Germany above. On aggregation, there must be some smoothing of these fluctuations, though not to an extent, as revealed in the previous section, that renders them as suitable surrogates for PIs. Had the results been more favorable, it would have been useful to attempt to characterize these “best” product classes for use in the compilation of UVIs in hybrid UVI/PI indices. Unexpectedly, they include three heterogeneous classes composed of “other” and “n.e.c.” products. There is also some concentration around plastic products and motor vehicle-related activities. But given the size of the discrepancies, these are not useful groupings.

Table 8.

CPA Four-Digit Classes in Percentile with the Least Discrepancy for Month-on-Month UVIs and PIs

article image

Not elsewhere classified.

European Coal and Steel Community.

The Planistat Report

Also of particular help in examining UVI and PI discrepancies at a disaggregated level is the extensive study PLANISTAT Europe Reports (Decoster, 2003a and 2003b) commissioned by Eurostat for European Member States. In particular, the second report provided a comparative analysis of import PIs and UVIs for Finland, Germany,8 the Netherlands, and Sweden. The monthly import indices used are those provided by these countries to Eurostat. The UVIs were extracted from the Comext database.9 The series are available at a three-digit level CPA and while results at aggregated levels are provided, they are unweighted and are not useful for our purposes. The series are monthly from January 1995 (= 100) to September 2001. Some of the results are provided and discussed in Silver (2007).10 For example, for Finland, of the 77 product groups at the three-digit level CPA for which import data were available, 17 percent had an average discrepancy between UVIs and XMPIs of less than 2.5 percent, and about another 40 percent between 2.5 and 5 percent. There was less difference between UVIs and PIs for Sweden with about one-third of three-digit product groups having a discrepancy of less than 2.5 percent. Bear in mind that a discrepancy of 0.025 implies that if the month-on-month change in the PI was zero, no change, then the UV index would take a value of a 2.5 percent change on average. The results in Silver (2007) demonstrate, as did Decoster (2003a and 2003b), that the average monthly discrepancy was unacceptable for any product group. Decoster (2003a, p. 9) found that PIs are more stable over time than UVIs, and that UVIs often display erratic behavior that PIs do not, concluding that

Any list of CPA categories for which UVIs are a priori acceptable as proxies for SPIs [import price indices] would be very short, especially as regards monthly data. It would include almost only aggregates and raw materials, even if sizable discrepancies between UVIs and SPIs are deemed acceptable. Apparently, any list of product categories for which short term UVIs are acceptable proxies for SPIs seems country specific. For a few low-tech products, for which quality changes are slow, UVI changes over the long term (several years) may be acceptable proxies for SPIs.

Use a More Detailed Stratification of Unit Values

A second possibility is to improve UVIs by more detailed stratification of the customs data. United Nations (1981) emphasized the need to stratify unit values to the (limited) extent possible and drew attention to doing so where possible by country of destination and size of batch, though see Párniczky (1974) on the limitations to this. Stratification is also possible for shipments by/to (major) establishments to/from given countries. However, the absence of highly detailed criteria by which to stratify unit values precludes any benchmark as to what is a reliable UVI. However, such experiments can be undertaken for consumer goods using highly detailed bar-code scanner data. Bradley (2005) examined the issue in some detail and found that even for detailed data of sales of cereal in 169 selected stores by 1,369 brands, aggregating unit values that distinguish a brand of tuna according to the week of purchase and store in which it is sold, as against simply aggregating unit values for the self-same brand and item, leads to substantial differences in the results. Silver and Webb (2002) took (brand and) model numbers for washing machines, dishwashers, vacuum cleaners, television sets, cameras, and personal computers, and compared unit value changes for the same models over different store types, finding quite different results when aggregating with and without store type as a variable. Haan and Opperdoes (1999) undertook a similar study on coffee, further apportioning their data according to the week of the month the data relates to, again finding unit value bias. Given such bias at this fine level of detail for aggregating identical items, it is hard to imagine disaggregated unit values based on customs returns being robust to unit value bias.

Use Other Country Data or Global Product PIs

An alternative to using UVIs is to use corresponding series from other countries, for example, an export PI of personal computers from the United States to proxy an import PI, or global commodity PIs to proxy exports or imports. The assumption is that there is a global market in which countries are price takers with little to no price discrimination between countries. In advocating stratification by country of origin/destination United Nations (1981) implicitly argued against this as a general strategy. However, there may well be product areas for which this is useful. It will not, of course, be a panacea for the measurement of trade PIs.

Different Formulas

PIs and UVIs are compiled in two stages. The first stage is the price relative (PIs) or unit value change (UVIs) at the elementary level of aggregation, to form elementary indices. The second stage is the weighted aggregation of these elementary indices. PIs and UVIs may be compiled using different formulas at this second stage, so differences in the results may in part be due to formula differences. Data were not available to recompile the indices to identify the effect of such formulas’ differences. Some insights are available for Germany.11 Germany is in the fortunate position of having import PIs, import deflators of the national accounts, and UVIs.12 The import PIs are of the Laspeyres type and refer to the year 2000. The Laspeyres principle is applied, however, only to the basket of goods, but not to the countries of origin, meaning that any shifts to low-cost producers will not be captured by the import PI. The national accounts deflators are annually chained Paasche indices, and the UVIs are Paasche indices referring to the year 2000. The product-specific PIs used for the compilation of the national accounts deflators are taken from the price statistics. Hence, the main difference between the import PI and the import deflator is to be found in the index formula.

In the years 2000-05, the UVI displayed a decline of 1.8 percent pa, whereas the import PI increased slightly and the import deflator decreased less strongly (+ 0.3 and—0.8, respectively). Taking the geometric average of the change in the import price deflator and the import PI gives an estimate of 0.2 percent as the “true” annual change in import prices, implying that the German UVI is significantly distorted downward.

Bear in mind, we are comparing Paasche UVIs with Laspeyres PIs. Von der Lippe (2007) demonstrates how the components of such formula discrepancy may cancel and any differences would be the result of unit value bias.

Lack of Customs Data and UVIs within Monetary Unions and for Services

There remains a potential problem of customs data itself becoming unsuitable for measuring trade flows for some countries. Countries with customs/monetary unions may abandon or limit the requirements on trade within the union to be documented. Furthermore, with services and e-commerce making up an increasing share of trade, customs data on merchandise trade will be unsuitable as the sole data source. Establishment-based sources for external trade price data have become the only practical option in these cases (though trade within customs unions may well be measured as a by-product of administering, for example, value-added taxes).

Use Deletion Routines for Unusual Price Changes

Of widespread use in the compilation of UVIs are deletion routines. This is because much of the data from customs records on unit value changes are extreme outliers and have to be discarded. Some of these arise from absent or poor quantity data. In other cases, it is due to unit value bias. Alterman (1991) estimated that the United States UVIs produced in 1985 were calculated for only 56 percent of the value of imports and 46 percent of the value of exports. For capital goods, the respective figures for imports and exports fell to 30.3 and 26.1 percent. The problems of such deletions are two-fold. First, the implicit effect on the sample representativeness and coverage. PIs are based on selected items from selected establishments with the purpose in mind that they are representative. Second, is that the deletion removes signal as opposed to noise. There is much evidence in CPI compilation, for example Hoffmann and Kurz-Kim (2006), that price changes can be substantial, and irregular, with long periods of constant prices followed by relatively large catch-up price changes. These large price increases may be deleted by outlier detection routines, resulting in UVIs that are unduly stable.

The Resource Constraint

A main reason why countries do not compile PIs is the cost of doing so. United Nations (1981) recognized the superiority of PIs by recommending well-endowed countries compile them, while advising countries with limited resources to compile UVIs. Countries require PIs not only for trade flows but also for the deflation of output, intermediate, and final consumption of goods and services by resident units. In particular, an output producer price index (PPI) is required that measures the changes in the prices of output of resident establishments. PPIs are compiled by selecting representative items from major/representative establishments and comparing the prices of like with like over time. Such output covers the domestic and export market (ILO and others, 2004b). For a self-standing export PI, there would be a need to identify price changes from such establishments for foreign markets as well as overall output and, as necessary, expand the sample size to ensure those establishments serving foreign markets are included in a representative manner. In some instances, specialist import/export wholesalers may be an efficient contact. Poorer countries have fewer establishments serving foreign markets with large proportions of exports usually being the responsibility of a relatively small number of establishments. Similar arguments apply to imports. Establishment-based trade PIs are but an extension of establishment-based price surveys for producer prices. There are resource costs to both PPIs and, by extension, to trade PIs. But they have their benefits that are the proper measurement of the major economic flows affecting the country, to allow for appropriate policy responses when necessary.

IV. Conclusions

There has been a long-held view that UVIs based on customs data can seriously misrepresent price changes as measured by PIs. The evidence in Section II of this paper supports that view: UVIs were found to seriously mislead in the sense that discrepancies between UVIs and PIs were substantial; changes could not be relied upon to have the same sign; there was no evidence of long-run (cointegrating) relationships between PIs and UVIs; and UVIs were of little help in predicting PIs. The findings held both for month-on-month and month-on-12-month changes. The marked unreliability of UVIs as measures of export and import price inflation was surpassed by the unreliability of the ToT indices based upon them. ToT indices based on UVIs failed with regard to the substantial magnitude of the discrepancy with PI-based ones, the wrong sign, absence of long-run relationship, and poor predictive value.

The results from using UVIs to measure the ToT effect, as part of a measure of real national income, and to deflate import and export current period values to derive volume measure were seriously misleading when compared with those from using PIs.

We reiterate the caveat to these findings at the start of this paper. The evidence presented here is limited to two countries that compile both PIs and UVIs, although other studies have similar conclusions. It is also limited by the fact that the deficiencies in UVIs are not measured against a perfect benchmark, the PIs themselves having deficiencies. Yet, as outlined above, UVIs suffer mainly from not comparing the prices of like with like, but establishment-based PIs do so. Furthermore, the coverage of PIs is by design representative, but the coverage of UVIs results from a substantial discarding of outliers. This and other studies asked how well UVIs stand up against PIs designed to overcome their major failings and the answer is that that they do not.

We then turned to the question of what can be done. The answer is to commence as soon as possible a program of establishment-based survey price collection. In Section III, we demonstrated that at the four-digit CPC level individual UVI series were still misleading. We would advocate a move from UVIs to establishment survey PIs. We recognize that there are resource costs involved and such a move involve a transitional utilization of hybrid indices, using PIs for the “low-hanging fruit” of the relatively small number of establishments responsible for a relatively large proportion of trade. In Section III, we also argued that customs data were by nature limited to the extent that it could benefit from further stratification. On a positive note, we stated that other country indices or global product prices may play a useful role, but this was not a panacea. The fact that our comparisons between UVIs and PIs were not pure was reiterated, and we then argued that customs and monetary unions and the increasing role of services in world trade give rise to the further cause of concern over a reliance on customs data. The main advantage of customs data had been argued to be their superior coverage of transactions and relatively low resource cost. We also argued that the extent of deletions gives rise to concern over the representativeness of UVIs and potential bias in deletion of some of the signal. As regards the resource constraint, the development of establishment-based surveys was identified as a natural part of the development of a system of producer price indices (PPIs), with a smaller resource demand on countries with less-developed import and export markets. Indeed, it seems apparent that a disservice is being done to countries by advocating the cheaper alternative of UVIs.


  • Alterman, William, 1991, “Price Trends in U.S. Trade: New Data, New Insights,” in International Economic Transactions, ed. by Peter Hooper and J. David Richardson (Chicago, University of Chicago Press).

    • Search Google Scholar
    • Export Citation
  • Angermann, Oswald, 1980, “External Terms of Trade of the Federal Republic of Germany Using Different Methods of Deflation,” Review of Income and Wealth, Vol. 26, No. 4 (December), pp. 36785.

    • Search Google Scholar
    • Export Citation
  • Balk, B.M., 1998, “On the Use of Unit Value Indices as Consumer Price Subindices,” in Proceedings of the Fourth Meeting of the International Working Group on Price Indices (Washington, U.S. Bureau of Labor Statistics). Available on the Internet at:

    • Search Google Scholar
    • Export Citation
  • Bradley, Ralph, 2005, “Pitfalls of Using Unit Values as a Price Measure or Price Index,” Journal of Economic and Social Measurement, Vol. 30, No. 1, pp. 3961.

    • Search Google Scholar
    • Export Citation
  • Decoster, Renaud, 2003a, “Import and Export Price Indices: A Comparison of Import Unit Value Indices and Import Specific Price Indices for Four EU Member States, Second Report,” Study Prepared for Eurostat Unit C-4: Methodology, Nomenclature and Statistics of External and Intra-Community Trade (Paris, PLANISTAT Europe).

    • Search Google Scholar
    • Export Citation
  • Decoster, Renaud,—, 2003b, Import and Export Price Indices: Final Report, Study Performed for Eurostat Unit 0074 C-4: Methodology, Nomenclature and Statistics of External and Intra-Community Trade (Paris, PLANISTAT Europe).

    • Search Google Scholar
    • Export Citation
  • Haan De, Jan, and Eddy Opperdoes, 1999, “Estimation of the Coffee Price Index Using Scanner Data: Simulation of Official Practices,” in Proceedings of the Third International Conference on Price Indices, ed. by B.M. Balk (Voorburg, Statistics Netherlands).

    • Search Google Scholar
    • Export Citation
  • Hoffmann, Johannes, and Jeong-Ryeol Kurz-Kim, 2006, Consumer Price Adjustment Under the Microscope: Germany in a Period of Low Inflation, Deutsche Bundesbank, Discussion Paper Series 1: Economic Studies, No. 16/2006.

    • Search Google Scholar
    • Export Citation
  • International Labor Organization (ILO), International Monetary Fund, Organization for Economic Cooperation and Development, Eurostat, United Nations, World Bank, 2004a, Consumer Price Index Manual: Theory and Practice (Geneva, International Labor Organization). Available on the Internet at:

    • Search Google Scholar
    • Export Citation
  • International Labor Organization (ILO), International Monetary Fund, Organization for Economic Cooperation and Development, UN Economic Commission for Europe, and World Bank, 2004b, Producer Price Index Manual: Theory and Practice (Washington, International Monetary Fund). Available on the Internet at:

    • Search Google Scholar
    • Export Citation
  • Konüs, A.A., 1924, “The Problem of the True Cost of Living Index,” English version published in Econometrica, Vol. 7, No. 1, pp. 1029.

    • Search Google Scholar
    • Export Citation
  • Kravis, Irving B., and Robert E. Lipsey, 1971, Price Competitiveness in World Trade, Studies in International Economic Relations, Vol. 6 (New York, National Bureau of Economic Research).

    • Search Google Scholar
    • Export Citation
  • Kravis, Irving B., and Robert E. Lipsey,—, 1985, “Prices and Terms of Trade for Developed-Country Exports of Manufactured Goods,” NBER Working Papers: No. 0774 (Cambridge, Massachusetts, National Bureau of Economic Research).

    • Search Google Scholar
    • Export Citation
  • Párniczky, G., 1974, “Some Problems of Price Measurement in External Trade Statistics,” Acta Oeconomica, Vol. 12, No. 2, pp. 22940.

    • Search Google Scholar
    • Export Citation
  • Ruffles, David, and Kevin Williamson, 1997, “Deflation of Trade in Goods Statistics: Derivation of Price and Volume Measures from Current Price Values,” Economic Trends, Vol. 521 (April). Reproduced in Office for National Statistics (ONS), Economic Trends Digest of Articles, No. 1, pp. 11116 (London: ONS).

    • Search Google Scholar
    • Export Citation
  • Silver, Mick, 2007, “Do Unit Value Export, Import, and Terms of Trade Indices Represent or Misrepresent Price Indices?IMF Working Paper 07/121 (Washington, International Monetary Fund).

    • Search Google Scholar
    • Export Citation
  • Silver, Mick,—, 2008, “An Index Number Formula Problem: The Aggregation of Broadly Comparable Items,” paper presented at the 2008 World Congress on National Accounts and Economic Performance Measures for Nations, May 12-17, Washington. Available on the Internet at:

    • Search Google Scholar
    • Export Citation
  • Silver, Mick,—, and Khashi Mahdavy, 1989, “The Measurement of a Nation’s Terms of Trade Effect and Real National Disposable Income within a National Accounting Framework,” Journal of the Royal Statistical Society, Series A, Vol. 152, Part 1, pp. 87107.

    • Search Google Scholar
    • Export Citation
  • Silver, Mick—, and Bruce Webb, 2002, “The Measurement of Inflation: Aggregation at the Basic Level,” Journal of Economic and Social Measurement, Vol. 28, No. 1-2, pp. 2136.

    • Search Google Scholar
    • Export Citation
  • United Nations, Department of International Economic and Social Affairs, 1981, Strategies for Price and Quantity Measurement in External Trade, Statistical Papers, Series M, No. 69 (New York, United Nations).

    • Search Google Scholar
    • Export Citation
  • Silver, Mick—, 1983, Price and Quantity Measurement in External Trade: Two Studies of National Practice, Statistical Papers, Series M, No. 76 (New York, United Nations).

    • Search Google Scholar
    • Export Citation
  • Von der Lippe, Peter, 2007, “Price Indices and Unit Value Indices in German Foreign Trade Statistics” (unpublished: Germany, University of Duisburg-Essen).

    • Search Google Scholar
    • Export Citation

Mick Silver is a senior economist in the IMF’s Statistics Department. This paper was originally prepared as a background paper to the draft “Export and Import Price Index (XMPI) Manual” developed under the aegis of the United Nations Inter-Secretariat Working Group on Price Statistics to update the existing United Nations (1981) guidelines. Acknowledgments are due to Renaud Decoster for providing summary statistics from the PLANISTAT Report, Mbaye Gueye (IMF) for aggregate International Financial Statistics data, and Klaus Pötzsch (Statistisches Bundesamt) for disaggregated data on Germany. The paper benefited from useful comments by Bert Balk (Statistics Netherlands), Matt Berger (ABS), Erwin Diewert (University of British Columbia), Carsten Hansen (UN ECE), Peter Hill, Johannes Hoffmann (Deutsche Bundesbank), Hans-Albert Leifer (Deutsche Bundesbank), Ronald Johnson (U.S. BLS), Kim Zieschang (IMF), and an anonymous referee.


The empirical evidence is of substantial volatility with unit value indices, on aggregate, generally falling below their corresponding PIs.


The main rationale for unit value indices was the limited resources required to compile them. United Nations (1981) laid down a strategy for countries with a tight budget; they should only use unit value indices, with disaggregation by county of origin/destination, where deemed appropriate. Well-endowed countries were advised to use establishment-based price surveys, possibly jointly with unit value indices. United Nations (1983) provided case studies on the development and implementation of price and unit value indices.


The European Commission Short-Term Statistics Council Regulation 1165/98 amended by 1158/2005 introduced requirements for the compilation of import and export price indices based on price surveys.


Economic theory allows a theoretically “true” index to be defined under assumptions of (competitive) optimizing behavior on the part of economic agents and related (not independent) prices and quantities. Actual index number formulas can be evaluated against their theoretical counterparts and also against a class of superlative indices that have good approximation properties to a well-defined theoretical economic index. This approach is based on the theory of the cost of living index developed by Konüs (1924) and used in the consumer price index (CPI) and PPI counterparts to this manual, ILO and others (2004a and 2004b).


Von der Lippe (2007) shows that adjustment for quality change is one reason why price indices are less volatile than unit value indices.


The reference to the 2008 SNA is to the final draft of Volume 1 (Chapters 1–17) of the updated System of National Accounts adopted by the 39th session of the United Nations Statistical Commission, February 26–29, 2008, and available at The 2008 SNA is an updated version of the 1993 SNA published by the Commission of the European Communities, International Monetary Fund, Organization for Economic Cooperation and Development, United Nations, and World Bank.


Von der Lippe (2007) in a study of German data uses Σm-1M(UVIm-PIm)/M that is differences in the index number levels which understate the mean differences as positive and negative differences to some extent cancel. With inflation, it also gives more importance to later period data (higher index levels) than data from earlier periods. Yet, it contains interesting information on the higher levels of volatility of unit value indices compared with that of price indices.


Data were not available at a detailed level of aggregation for Germany.


UVIs are subject to outlier detection and revision and the series available in Comtext may differ from those available from the individual countries in this regard.


The PLANISTAT report was undertaken by Renaud Decoster. The results provided here are based on the worksheets of summary measures for the individual series, provided to the author of this chapter by Mr. Decoster. The author acknowledges Mr. Decoster’s help and advice. The above tables do not appear in the report, but are based on the data series used for the report. The conclusions drawn here and in the report are very similar and differ only in that a less favorable consideration is given in the report to UVIs than here.


UVIs are compiled in Japan using a Fisher index and the trade price indices (from their Corporate Goods Price Index) using a chained Laspeyres index, although there is some lag in the adoption of the most recent period’s weights.


Data and this account on Germany are from private correspondence with Johannes Hoffmann and Hans-Albert Leifer, Deutsche Bundesbank, December 2006.

IMF Staff Papers, Volume 56, No. 2
Author: International Monetary Fund. Research Dept.