## 1.     Export unit value and price indices for Germany

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### III. Main conclusions on UVIs versus PIs
- Unit value indexes (UVIs) have no well-defined relationship over time to narrow specification price indexes (PIs); substantial discrepancies in direction and magnitude exist.
- UVIs have no predictive power for narrow specification PIs.
- For terms of trade (ToT) indices the discrepancies are worse.
- Measures of the terms of trade effect (for real national income) and deflated volume changes differ vastly when measured using UVIs as opposed to PIs.
- No evidence of homogeneous product classes for which UVIs may be reliably used.
- Significant unit value bias arises within strata defined at levels of detail well beyond that available in customs systems.
- UVIs apply only to trade subject to customs administration and cannot be compiled for trade within economic unions.

### I. Purpose, context, and international recommendations
- Purpose:
  - Assess whether export and import UVIs derived from customs data represent or misrepresent export and import price changes.
  - Examine uses of UVIs: short-term indicators of inflation transmission; measure changes in terms of trade; deflators of export and import values.
- Context:
  - United Nations (1981) and System of National Accounts 1993 note limitations of UVIs; draft XMPI Manual focuses on establishment survey pricing, limiting UVIs to very strictly homogeneous products.
- UN (1981) guidance summaries:
  - Sole use of UVIs appropriate for budget-constrained authorities with stratification and exclusions rules.
  - Average-budget countries: use customs documentation with product analysts to detect abnormalities.
  - Well-endowed countries: use establishment-based price surveys, possibly jointly with UVIs.

### IV. Sources and mechanisms of UVI bias
- Causes of bias:
  - Compositional mix changes in quantities and quality mix; customs documents lack sufficient product detail to adjust for quality.
  - Non-comparability of "like with like" between periods.
  - Problems with quantities and units reported in customs returns; changing measurement units can change UVI results.
  - Deletions/outlier routines can remove signal as well as noise, reducing coverage substantially.
  - Changes in data environment: customs/monetary unions, intra-union trade, services and e-commerce growth reduce applicability of customs-based UVIs.
- Formula and aggregation issues:
  - PIs and UVIs may use different aggregation formulas (Laspeyres, Paasche, Fisher, chained indices), producing formula-driven differences.
  - Example: German import price indices are Laspeyres referring to year 2000; national accounts deflators are annually chained Paasche; unit value indices are Paasche referring to year 2000.
- Conditions for zero unit value bias (Balk (1998); cited):
  - (1) all base period prices p0m equal each other and all current period prices p1n equal each other;
  - (2) all quantity relatives q1m/q0m are equal to each other;
  - (3) no correlation between p0m and q1m/q0m, and no correlation between p1n and q1m/q0m.
  - These conditions are highly restrictive and unlikely in practice.

### V. Empirical evidence: Germany and Japan (monthly data 1996:7–2006:9)
- Volatility and discrepancies (short-run, month-on-month and month-on-12 month):
  - For Germany UVIs are clearly much more volatile than PIs; for Japan the relative volatility of UVIs is much less marked.
  - Mean month-on-month discrepancy for imports to Germany: 1.1 percent.
  - Standard deviation for these month-on-month changes (Germany imports): 1.0 percent.
  - Maximum month-on-month discrepancy observed (Germany imports): 7.3 percentage points.
  - Month–on-12 month: with a mean 12 month PI change for German imports of 4.75 percent, an average discrepancy of 1.8 percent and standard deviation of 1.6 percent.
- Sign agreement:
  - About 25 percent of month-on-month comparisons the signs differ (UVIs and PIs indicate opposite directions in one quarter of comparisons).
  - Month-on-12 month results are better but unreliable in some series (e.g., German exports).
- Cointegration and prediction:
  - Unit root null rejected at 5 percent level for all month-on-month comparisons and for all month-on-12 month comparisons except German exports.
  - UVIs and PIs are generally not I(1); index series themselves are I(1).
  - Cointegration tests: p-values exceed 0.05; linear combinations of UVI and PI are not I(0) — UVIs and PIs are not cointegrated.
  - Predictive regressions using lagged UVIs: F-test for null that all lag coefficients are zero is rejected in three out of four cases for month-on-month indices and in all cases for month-on-12 month changes; predictive power exists but is weak with wide predictive intervals (example: 95 percent interval for German imports is 1.8±percent).
  - Granger-causality tests: in half the cases lagged UVIs contain no predictive power over and above lagged PIs; tests do not establish UVIs Granger-cause PIs (nor PIs Granger-cause UVIs consistently).

### VI. Terms of trade (ToT) findings and ToT effect
- ToT measurement issues:
  - ToT measured as ratio of export price index to import price index; using UVIs as surrogates can lead to bias cancellation if biases are equal, or compounding if biases differ.
- Discrepancy magnitudes:
  - Mean month-on–month discrepancy for ToT changes for Germany: 1.3 percent (compared with 1.1 and 0.9 percent for imports and exports respectively).
  - For month-on-12 month changes the ToT discrepancy for Japan was 3.7 percent compared to 2.4 and 2.5 percent for imports and exports respectively.
  - Japan ToT example implication: if the ToT PI change was unity, the ToT UVI index would on average show a month–on-month change of 3.7 percent with standard deviation over time of 10 percent (0.10) and maximum of 70 percent (0.70).
- Sign agreement for ToT:
  - Month-on-month ToT indices had the wrong sign in over one-third of month-on-month comparisons.
  - Japan’s month-on-12 month ToT series had the wrong sign in 22 percent of cases while export and import series had wrong sign in 15 and 4 percent respectively.
- Cointegration and prediction for ToT:
  - ToT indices measured by UVIs and PIs do not have unit roots and thus are not cointegrated.
  - Lagged ToT UVIs have some predictive information relative to ToT PIs but it is very weak; for Germany lagged ToT UVIs have no predictive ability over ToT PIs, while for Japan lagged UVIs have some such ability.
- ToT effect example (Table 9): in 2005 Japan’s trade balance of 6,956 billion Yen is eliminated by the adverse change in its terms of trade when using PIs, but only halved when using UVIs.

### VII. Long-run changes and use as deflators (selected results)
- Examples 1999–2005 (Table 10):
  - Germany Exports (Billion Euros at constant 1999 prices): Unit values 591.5 (1999) to 799.0 (2005), Percentage change 35.1; Price indices 591.5 (1999) to 857.9 (2005), Percentage change 45.0.
  - Germany Imports (Billion Euros at constant 1999 prices): Unit values 796.3 (1999) to 785.5 (2005), Percentage change -1.4; Price indices 796.3 (1999) to 705.2 (2005), Percentage change -11.4.
  - Japan Exports (Billion at constant 1999 prices): Unit values 1,144.0 (1999) to 650.9 (2005), Percentage change -43.2; Price indices 1,144.0 (1999) to 674.1 (2005), Percentage change -41.0.
  - Japan Imports (Billion at constant 1999 prices): Unit values 4,957.0 (1999) to 4,353.9 (2005), Percentage change -16.3; Price indices 4,957.0 (1999) to 2,574.6 (2005), Percentage change -19.1.
- Tests of long-run mean log inflation rate differences (t-tests, Annex 1):
  - Exports for Germany: t = 0.828; p-value = 0.41.
  - Imports for Germany: t = 0.219; p-value = 0.83.
  - Exports for Japan: t = -1.554; p-value = 0.12.
  - Imports for Japan: t = 0.742; p-value = 0.46.
  - ToT for Germany: t = 0.463; p-value = 0.64.
  - ToT for Japan: t = -1.946; p-value = 0.052 (not rejected at conventional levels).

### VIII. Quantified summary statistics (selected table figures)
- Table 1 (Absolute value of ratio of UVI to PI: [(UV/PI)-1], selected entries):
  - Month-on-month (Germany Import): Mean 0.011; Standard deviation 0.010; Maximum 0.073; Root mean squared error 0.014; Mean absolute deviation 0.011.
  - Month-on-month (Japan Export): Mean 0.013; Standard deviation 0.010; Maximum 0.055; Root mean squared error 0.016; Mean absolute deviation 0.013.
  - Month-on-12 month (Germany Import): Mean 0.018; Standard deviation 0.016; Maximum 0.096; Root mean squared error 0.024; Mean absolute deviation 0.018.
  - Month-on-12 month (Japan Export): Mean 0.025; Standard deviation 0.019; Maximum 0.099; Root mean squared error 0.031; Mean absolute deviation 0.025.
- Table 2 (UVI and PI: percentage of changes of same and different sign), Month-on-month (selected):
  - Exports (Germany): same sign both positive 41.7; both negative 16.6; different signs UV positive : PI negative 12.5; UV negative : PI positive 29.2.
  - Imports (Japan): same sign both positive 41.8; both negative 21.3; different signs UV positive : PI negative 11.1; UV negative : PI positive 16.8.
- Table 5 (ToT indices: discrepancy between UVIs and PIs):
  - Month-on-month (Germany): Mean 0.013; Standard deviation 0.010; Maximum 0.070; Root mean squared error 0.016.
  - Month-on-12 month (Japan): Mean 0.037; Standard deviation 0.027; Maximum 0.183; Root mean squared error 0.046.

### IX. Disaggregated evidence and the (lack of) homogeneous classes
- German CPA 4-digit analysis (January 2000–November 2006):
  - 150 class series available for both UVIs and PIs; 15 classes in the lowest percentile identified as “best”.
  - Best two product classes (manufacture of motor vehicles and manufacture of pulp): mean month-on-month discrepancies of 2.00 percent.
  - Bottom of the best percentile (manufacture of fertilizer and nitrogen compounds): discrepancy on average of 4.00 percent.
  - Standard deviations for best classes: 6 and 7 percent; for worst end of best percentile: 15 percent.
  - Aggregation smooths some fluctuations but not enough to render UVIs suitable surrogates for PIs.
- PLANISTAT country 3-digit results (summary):
  - Finland (77 product groups): 17 percent had average discrepancy < 2.5 percent; about another 40 percent between 2.5 and 5 percent.
  - Sweden: about one-third of 3-digit product groups had discrepancy < 2.5 percent.
  - Large shares of product groups have discrepancies exceeding 2.5 percent: 83, 87, and 66 percent for Finland, Netherlands, and Sweden respectively.
- Table 11 selected CPA 4-digit classes with least month-on-month discrepancy:
  - Manufacture of motor vehicles CPA-3410: Mean 0.0197; Maximum 0.0601; Minimum 0.0009; Standard deviation 0.0153.
  - Manufacture of pulp CPA-2111: Mean 0.0197; Maximum 0.0664; Minimum 0.0003; Standard deviation 0.0148.
  - Manufacture of motor vehicles parts and accessories CPA-3430: Mean 0.0260; Maximum 0.1266; Minimum 0.0001; Standard deviation 0.0212.

### X. Predictive and cointegration test evidence (selected)
- Predictive regressions (Table 4):
  - Mixed evidence: PIs often Granger-cause UVIs strongly (examples of PI→UVI F-statistics reported: 9.133, 5.969, 17.505, 18.258, 27.304, 19.824, 57.566, 62.057 with p-values 0.000.00…).
  - UVIs rarely Granger-cause PIs; some UVI→PI F-statistics shown include 0.339, 2.491, 2.571, 0.781, 0.405, 0.573, 113.486, 3.160 with limited significance.
- Unit root and cointegration tests (Tables 3 and 7):
  - Monthly changes often reject unit root nulls; cointegration between UVIs and PIs generally absent or weak with many p-values not supporting cointegration.

### XI. Policy and practical recommendations
- Primary recommendation:
  - Commence as soon as possible a program of establishment-based survey price collection to compile trade price indices (PIs). Establishment-based PIs compare like with like and are designed for representative coverage.
- On UVIs:
  - Avoid overreliance on UVIs as a cheaper substitute; UVIs are demonstrably deficient and can mislead economic analysis.
  - Hybrid strategies (UVI/PI) that use UVIs broadly and PIs selectively are unlikely to be reliable unless carefully targeted to genuinely homogeneous products.
- Improvements to UVIs where used:
  - Stratify customs data more finely (country of origin/destination, size of batch, establishment identifiers, time strata such as week of purchase) recognizing practical limitations.
  - Review deletion/outlier routines to avoid deleting substantive price changes that PIs would capture.
  - Harmonize index formulas where possible or assess formula-driven biases (Laspeyres vs Paasche vs Fisher vs chained indices).
- Interim/alternative approaches:
  - Use other-country or global product price series as temporary proxies in select product areas where global price-taking assumptions are plausible.
- Resource-constrained advice:
  - Prioritize development of establishment-based surveys as part of broader price-index systems; trade PIs are a logical extension of PPIs and offer more reliable measurement for policy.

### XII. Appendix — statistical test setup for long-run differences
- Two price series p_t and P_t with p_0 = P_0 ≡ 1.
- Differential growth representation:
  - p_t = α_1 α_2 ... α_t P_t ; t = 1,...,T.
  - p_t/p_{t−1} = α_t (P_t/P_{t−1}) ; t = 1,...,T.
- Logarithmic rates:
  - y_t ≡ ln(p_t/p_{t−1}) ; Y_t ≡ ln(P_t/P_{t−1}) ; t = 1,...,T.
- Difference series and stochastic model:
  - Z_t ≡ y_t − Y_t = β_t ; β_t ≡ ln α_t ; convert to Z_t = β + ε_t with ε_t iid normal(0,var).
  - Estimator for β is the average of the Z_t (difference of average log growth rates); test H0: β = 0.
- Extension to terms of trade:
  - Define y_{TT t} and Y_{TT t} as logarithmic growth rates of terms of trade; Z_{TT t} ≡ y_{TT t} − Y_{TT t} = β_{TT} + ε_{TT t}.
  - β_{TT} equals 0 implies UVIs and PIs give the same long-run ToT changes; estimator β_{TT}* = β_X* − β_M*.

*Content derived from _wp07121.*

### 1.     Export unit value and price indices for Germany.............................................................23

### 1.     Export unit value and price indices for Germany.............................................................23

### Chapter structure and major sections
- Section 1: Export unit value and price indices for Germany (page 23).
- Section 2: Export unit value and price indices for Japan (page 23).
- Section 3: Import unit value and price indices for Germany (page 23).
- Section 4: Import unit value and price indices for Japan (page 24).

### Tables included in this content unit (by table number and title)
- Table 1: Average discrepancy between import unit value and price indices (page 24).
- Table 2: UVI and PI: Percentage of changes of same and different sign (page 24).
- Table 3: Unit root tests and cointegrating relationships between month-on-month and 12-month percentage change (page 25).
- Table 4: Predictive ability of UVIs in relation to Pis (page 26).
- Table 5: Terms of trade indices: Discrepancy between UVIs and PIs (page 26).
- Table 6: Terms of trade: Percentage of changes of same and different sign (page 26).
- Table 7: Terms of trade indices: Unit root and cointegration tests (page 27).
- Table 8: Terms of trade: Predictive ability of UVI in relation to PI (page 27).
- Table 9: Terms of trade effect: Previous year's prices (page 27).
- Table 10: Comparison of deflated exports and imports by UVIs and Pis (page 28).
- Table 11: CPA 4-digit classes in percentile with the least discrepancy for month-on-month UVIs and PIs (page 28).
- Table 12: Average discrepancy between import unit value and price indices: Absolute value of month-on-month percentage changes (page 29).

### Scope and focus (as indicated by headings)
- Comparative analysis of unit value indices (UVIs) and price indices (PIs) for exports and imports, with country focus on Germany and Japan.
- Examination of discrepancies between UVIs and PIs, including measures of average discrepancy and absolute month-on-month percentage changes.
- Statistical testing coverage: unit root tests, cointegration relationships for month-on-month and 12-month percentage changes.
- Predictive analysis: assessment of the predictive ability of UVIs relative to PIs for prices and terms of trade.
- Terms of trade analysis: discrepancies, percentage-change sign comparisons, unit-root and cointegration testing, and the effect of previous year's prices.
- Detailed product-level investigation: CPA 4-digit class percentile analysis for least discrepancy between month-on-month UVIs and PIs.
- Comparisons of deflated trade flows using UVIs versus PIs.

*Source: _wp07121 - 1.     Export unit value and price indices for Germany (PDF chapter/section).*

### References..............................................................................................................

### _wp07121 - References..............................................................................................................

### I. INTRODUCTION
- Main purpose: consider whether export and import unit value indices derived from customs data represent or misrepresent export and import price changes.
- Uses of unit value indices (UVIs):
  - Short-term indicators of inflation transmission.
  - Measure changes in a country’s terms of trade (effect).
  - Deflators of export and import values to yield measures of changes in export and import volumes.
- Primary concern: known biases in UVIs and whether these biases make UVIs unsuitable as proxies for narrow specification price indices collected from establishments.
- Key conclusions stated:
  - Indexes of unit values have no well-defined relationship over time to desired narrow specification price indexes; substantial discrepancies in direction and magnitude exist.
  - Unit value indexes have no predictive power for narrow specification price indexes.
  - For terms of trade indices the discrepancies are worse.
  - Measures of the terms of trade effect (for real national income) and deflated volume changes are vastly different when measured using unit value indices as opposed to price indices.
  - No evidence of homogeneous product classes for which unit value indices may be reliably used.
  - Significant unit value bias arises within strata defined at levels of detail well beyond that available in customs systems.
  - Unit values are only applicable to trade subject to customs administration, and thus cannot be compiled for trade within economic unions.
- Context and history:
  - Few deny (including United Nations (1981)) that narrow specification price indexes provide the best measures of relative price change and that customs unit values are potentially significantly biased.
  - Unit values persist because they are by-products of customs systems and have relatively low incremental cost versus establishment price surveys.
  - The paper adds weight to recommending against using UVIs as proxies for well-defined price indexes.

### II. INTERNATIONAL RECOMMENDATIONS
- Background: paper is a background paper to the draft Export and Import Price Index (XMPI) Manual developed under the United Nations Inter-Secretariat Working Group on Price Statistics (IWGPS) to update United Nations (1981).
- Major departure in draft Manual: focus largely on the establishment survey pricing approach (prices of well specified products from establishments), limiting use of UVIs to very strictly homogeneous products.
- United Nations (1981) guidance:
  - Sole use of UVIs was proposed as appropriate for statistical authorities with resource constraints.
  - Strategy for budget-constrained countries: use unit values with disaggregation by country of origin/destination where appropriate; exclude items with unit value changes outside specified bounds unless exclusions amount to at least half the value of the classification category; treat “machinery and transport equipment” and “miscellaneous manufacturing” specially.
  - Advice for average-budget countries: rely on customs documentation but use product analysts to detect abnormal changes; intensively analyze unit value distributions and question extreme values/changes.
  - Advice for well-endowed countries: use establishment-based price surveys, possibly jointly with UVIs.
- System of National Accounts 1993: notes unit value indices “cannot therefore be expected to provide good measures of average price changes over time.” (Para. 16.13).

### III. UNIT VALUE INDICES AND THEIR BIAS
- Structure: Section outlines bias from compositional mix changes (A), formal properties/tests (B), and summary of concerns (C).

A. Unit Value Bias Illustrated
- United Nations (1981) refrigerator example:
  - Assumptions: prices double for each size group; shift in quantities toward larger refrigerators; total quantity same over time.
  - Data (as given):
    - Period "Now": q = 2, 3, 5; p = 2, 4, 6; v = 4, 12, 30; All sizes q = 10, p = 4.6, v = 46
    - Period "Then": q = 5, 3, 2; p = 1, 2, 3; v = 5, 6, 6; All sizes q = 10, p = 1.7, v = 17
  - Weighted average of size-group price changes = 2.0.
  - Unit value change = 4.6/1.7 = 2.71.
  - Conclusion: upwards bias in the UVI due to compositional shift toward more expensive refrigerators.

B. Unit Value Indices: the Test Approach
- Unit value index definition (as presented): P_U(p0,p1,q0,q1) ≡ (formula shown in source). (Equation (1) included in source.)
- Failures of unit value index with respect to axiomatic tests:
  - Fails Proportionality Test: P(p,λp,q0,q1) = λ for λ > 0 only if relative quantities do not change (rare).
  - Fails Identity or Constant Prices Test: P(p,p,q0,q1) = 1 only if relative quantities do not change.
  - Succeeds Proportionality in current period prices test: P(p0,λp1,q0,q1) = λP(p0,p1,q0,q1) for λ > 0.
  - Fails Invariance to Changes in the Units of Measurement (commensurability) Test: changing measurement units for products can change the index.
  - Passes other tests: time reversal test, circularity test, and the product test.
- Consequences:
  - Price index affected by changes in relative quantities is a serious deficiency: fixed basket concept requires holding quantities constant.
  - Unit value index is not a proper price index unless applied to homogeneous products.
  - Choice of measurement units (e.g., items vs. weight) affects results, creating ambiguity.
  - Quality changes implicitly alter the unit of productive service or utility and bias the index; customs data lack quality characteristic detail compared with establishment data.
- Conditions for zero unit value bias (Balk (1998)):
  - (1) all base period prices p0m equal each other and all current period prices p1n equal each other;
  - (2) all quantity relatives q1m/q0m are equal to each other;
  - (3) no correlation between p0m and q1m/q0m, and no correlation between p1n and q1m/q0m.
  - These are highly restrictive and unlikely in practice.
- Bradley (2005) conclusion: UVI appropriate only under extreme conditions.

C. Unit Value Indices: the Cause for Concern
- Grounds for unreliability of UVIs:
  - Bias from compositional changes in quantities and quality mix; limited scope to reduce bias due to sparse variables on customs documents (class of size of order and country of origin/destination).
  - For unique/complex goods, model pricing possible in establishment surveys but not for UVIs.
  - Establishment surveys can better deal with quality change, temporarily missing values, and seasonal goods; UVIs cannot.
  - Quantities in customs returns and choice of units are often seriously problematic in practice.
  - Customs unions may limit intra-area trade data availability.
  - Increasing trade in services and e-trade is not subject to customs documentation.
  - UVIs rely heavily on outlier detection and deletion; deletions risk missing large price catch-ups and understating inflation.
- Advantages often cited for UVIs:
  - Coverage and relatively low resource cost.
- Limitations of UVIs as samples:
  - UVIs drawn as non-random samples and exclude products traded irregularly; products with no quantity reported (especially parts and machinery); low-value shipments; and erratic month-to-month changes.
  - Extent of such exclusions can be substantial (illustrated elsewhere in source).
- Establishment-based surveys:
  - Can be representative; often a small number of wholesalers/establishments account for much of total import/export value and, with cooperation, can be cost-effective and reliable.
  - Good sampling can realize accurate price change measures.
  - Value shares from customs data provide weights for establishment-based surveys.
- Reference to methodological guidance:
  - Silver (2006) (Chapter 11 of draft XMPI Manual) outlines sources of error and bias and methods to mitigate them, drawing on CPI and PPI compilation practices and manuals (ILO et al., 2004a and 2004b).
  - Trewin (2006) cited as an example of country practice.
- Von der Lippe (2007): adjustments for quality change help explain why price indices are less volatile than unit value indices.

### IV. EVIDENCE
- Terminology adopted: PI = establishment-survey based price index; UVI = customs-data based unit value index.
- Need to examine empirical evidence comparing UVIs and PIs where both are compiled.
- Evidence is limited:
  - Limited to countries compiling both UVIs and PIs.
  - Deficiencies in UVIs are not measured against a perfect benchmark; PIs themselves have deficiencies.
- Structure of evidence section: aggregate-level existing studies, new results for Germany and Japan, and further disaggregated results in Section V for Germany and some other European countries.
- Existing study example introduced:
  - Alterman (1991) compared price changes between March 1985 and June 1989 for the United States as measured by UVIs and by PIs based on establishment surveys that replaced them.
  - For imports, over this period, the PI increased by 20.8 percent and the UVI increased by (text continues in source).

*Italic line: Content derived from _wp07121 - References (source PDF excerpt).*

### 13.7 percent. For exports, the figures were much closer, 13.0 and 12.2 percent for the price

### _wp07121 - 13.7 percent. For exports, the figures were much closer, 13.0 and 12.2 percent for the price

### Key differences between Unit Value Indices (UVIs) and Price Indices (PIs)
- Export/import aggregate comparisons: 13.7 percent. For exports, the figures were 13.0 and 12.2 percent for the price survey and UVI respectively.
- Recalculation of price survey indices using UVI weights produced larger differences: a 20.6 percent and 16.4 percent increase for the import and export price indices respectively.
- The average (absolute quarter-on-quarter) UVI change for imports and exports respectively were 27 and 70 percent larger than the corresponding PI changes.
- Example implication for national accounts deflation (Alterman (1991)): the annualized second-quarter 1989 “real” trade deficit in March 1985 dollars would have been $128.4 billion if deflated by UVIs, but just $98.8 billion, 23 percent less, if deflated by the PIs.
- Historical findings cited:
  - Kravis and Lipsey (1971): prices of manufactured goods exported by developed countries to developing countries rose by 75 percent over about twenty years, compared to l4 percent shown by UVIs.
  - Kravis and Lipsey (1985): decrease in the terms of trade of manufactures relative to all primary products between 1953 and 1976 of over 36 percent using price indices, compared to 28 percent suggested by UVIs; with further quality correction the price data suggested a fall of over 45 percent, more than 50 percent greater than UVIs.

### B. Comparison for Germany and Japan: data and short-run indicator evidence
- Data: monthly data for 1996:7 to 2006:9 from the IMF’s International Financial Statistics (IFS).
- Short-run (month-on-month and month-on-12 month) findings:
  - For Germany UVIs are clearly much more volatile than PIs; for Japan the relative volatility of UVIs is much less marked.
  - Substantial discrepancies between PIs and UVIs for exports and imports in both countries; Japan shows periods where UVIs and PIs track each other but this breaks down.
- Summary statistics (month-on-month discrepancies):
  - Mean discrepancy for imports to Germany: 1.1 percent.
  - Standard deviation for these month-on-month changes: 1.0 percent.
  - Maximum month-on-month discrepancy observed: 7.3 percentage points.
  - Month–on-12 month: with a mean 12 month PI change for German imports of 4.75 percent, an average discrepancy of 1.8 percent and standard deviation of 1.6 percent.
- Sign agreement:
  - About 25 percent of month-on-month comparisons the signs differ (i.e., UVIs and PIs indicate opposite directions in one quarter of comparisons).
  - Month-on-12 month results are better but unreliable in some series (e.g., German exports).

### Cointegration and prediction
- Unit root / cointegration results:
  - Unit root null hypothesis rejected at 5 percent level for all month-on-month comparisons and for all month-on-12 month comparisons except German exports.
  - UVIs and PIs are generally not I(1); index series themselves are I(1).
  - Cointegration test statistics have p-values that exceed 0.05; the null hypothesis of a unit root in the cointegrating regression cannot be rejected and the linear combination of the unit value and price index is not I(0) — UVIs and PIs are not cointegrated.
- Prediction evidence (lagged UVIs predicting PIs):
  - Estimated relationship for each PI series using lagged UVIs; Table 4 shows the F-test for the null that all lag coefficients are zero is rejected in three out of four cases for month-on-month indices and in all cases for month-on-12 month changes.
  - Predictive power exists in most cases but is weak: predictive intervals are wide (example provided: the 95 percent interval for German imports is 1.8±percent).
  - Granger-causality (GC) tests: in half the cases lagged UVIs contain no predictive power over and above lagged PIs; tests do not establish that UVIs GC PIs (PIs do not GC UVIs either).

### Terms of trade (ToT) and ToT effect
- ToT measured as ratio of price index of exports to price index of imports; use of UVIs as surrogates can lead to bias cancellation if biases are equal, but can compound if biases differ.
- Discrepancies in ToT measures:
  - Mean month-on–month discrepancy for ToT changes for Germany: 1.3 percent (compared with 1.1 and 0.9 percent for imports and exports respectively).
  - For month-on-12 month changes the ToT discrepancy for Japan was 3.7 percent compared to 2.4 and 2.5 percent for imports and exports respectively.
  - ToT discrepancy for Japan implies that if the ToT PI change was unity, the ToT UVI index would on average show a month–on-month change of 3.7 percent with standard deviation over time of 10 percent (0.10) and maximum of 70 percent (0.70).
- Sign agreement for ToT:
  - Month-on-month ToT indices had the wrong sign in over one-third of month-on-month comparisons.
  - Japan’s month-on-12 month series had the wrong sign in 22 percent of cases while export and import series had the wrong sign in 15 and 4 percent respectively.
- Cointegration and prediction for ToT:
  - ToT indices measured by both UVIs and PIs do not have unit roots and thus are not cointegrated.
  - Lagged ToT UVIs have some predictive information relative to ToT PIs but it is very weak; for Germany lagged ToT UVIs have no predictive ability over ToT PIs, while for Japan lagged UVIs have some such ability.
- Terms of trade effect (trading gain/loss) calculation per SNA 1993:
  - Formula presented (equation (4) in text); interpretation emphasizes dependence on deflator choice.
  - Table 9 example: in 2005 Japan’s trade balance of 6,956 billion Yen is eliminated by the adverse change in its terms of trade when using PIs, but only halved when using UVIs.

### Long-run changes and use as deflators
- Table 10 example results (1999–2005):
  - Volume of exports by Japan increased by 50 percent when a UVI deflator is used, but the increase is halved when a PI is used.
  - Volume of imports by Germany was about constant over this period when a UVI deflator is used, but fell by about 10 percent when a PI deflator is used.
- Statistical tests of long-run mean log inflation rate differences (t-tests, Annex 1):
  - Exports for Germany: t = 0.828; p-value = 0.41 (null not rejected).
  - Imports for Germany: t = 0.219; p-value = 0.83 (null not rejected).
  - Exports for Japan: t = -1.554; p-value = 0.12 (null not rejected).
  - Imports for Japan: t = 0.742; p-value = 0.46 (null not rejected).
  - ToT for Germany: t = 0.463; p-value = 0.64 (null not rejected).
  - ToT for Japan: t = -1.946; p-value = 0.052 (null not rejected at conventional levels).
- Overall conclusion from Section B: export and import UVIs are inadequate surrogates for PIs when used in economic analysis (short- and long-run inflation, prediction, terms of trade, ToT effects, and as deflators). Evidence indicates UVIs can be seriously misleading.

### V. What is to be done? — policy/research options and disaggregated evidence
- Practical concern: UVIs are used by most countries; moving to PIs has resource consequences.
- Proposed approach: hybrid UVI/PI index — identify products prone to UVI bias and undertake price surveys only for those products.
- A. Use unit value sub-indices for homogeneous product groups: reliability of sub-indices
  - Disaggregated German data: export and import UVIs and PIs January 2000 to November 2006 at 4-digit CPA level.
  - 150 class series available for both UVIs and PIs; 15 classes in the lowest percentile identified as “best” (least average discrepancies).
  - Best two product classes (manufacture of motor vehicles and manufacture of pulp): mean month-on-month discrepancies of 2.00 percent.
  - Bottom of the best percentile (manufacture of fertilizer and nitrogen compounds): discrepancy on average of 4.00 percent.
  - Standard deviations: 6 and 7 percent for the best two classes; 15 percent for the worst end of the best percentile; maximums in Table 11 reflect serious volatility.
  - Aggregation smooths some fluctuations but not enough to render UVIs suitable surrogates for PIs.
  - The “best” product classes unexpectedly include heterogeneous “other” and “n.e.c.” classes; concentration around plastic products and motor vehicle related activities noted, but discrepancies remain too large for reliable substitution.
- Anecdotal confirmation from compilers:
  - Denmark example: coal considered homogeneous but UVIs were unpredictable and uncorrelated with price changes due to heterogeneity (energy content, cleaning/filtering, residual use).
- PLANISTAT Europe Reports (Decoster 2003a, 2003b) findings at 3-digit CPA:
  - For Finland: of 77 product groups, 17 percent had average discrepancy < 2.5 percent; about another 40 percent between 2.5 and 5 percent.
  - For Sweden: about one-third of 3-digit product groups had discrepancy < 2.5 percent.
  - Interpretation: a discrepancy of 0.025 implies if the month-on-month PI change was zero then the UVI would show a 2.5 percent change on average — potentially misleading.
  - Large shares of product groups have discrepancies exceeding 2.5 percent: 83, 87, and 66 percent of 3-digit groups in Finland, Netherlands, and Sweden respectively had discrepancies that on average exceeded 2.5 percent.
  - Table 12 average discrepancies for the three countries: 5.3, 5.4, and 4.1 respectively; minimum discrepancy for a 3-digit group reported (table material continues in source).

*Source: _wp07121 - 13.7 percent. For exports, the figures were much closer, 13.0 and 12.2 percent for the price (IMF working paper content provided).*

### 1.5 and 2 percent—at best still significant potential to mislead economists.

### _wp07121 - 1.5 and 2 percent—at best still significant potential to mislead economists.

### Key empirical findings on UVIs versus PIs
- UVIs were found to "seriously mislead" relative to price indices (PIs): discrepancies were substantial; changes could have different signs; there was no evidence of long-run (cointegrating) relationships between PIs and UVIs; and UVIs were of little help in predicting PIs. (Section VI)
- The unreliability of UVIs was greater still for terms of trade indices based on UVIs: substantial magnitude of discrepancy, wrong sign, absence of long-run relationship, and poor predictive value. (Section VI)
- Month-on-month and month-on-12 month comparisons both show poor correspondence between UVIs and PIs. (Section VI)

### Quantified discrepancies and volatility
- Table 12 analysis: figures cited are the mean discrepancy over the 68 month-on-month comparisons for January 1995 (=100) to September 2001. Standard deviations for each discrepancy across the 68 comparisons quantify volatility. The average dispersion is high: for each country the mean standard deviation over the groups exceeds the mean of the groups. (text)
- Finland: the very lowest dispersion over time of the month-on-month discrepancy for a 3-digit group is for Finland at 1.9 percent, allowing an approximately 95 percent plus or minus range of 2 x 1.9=3.8 percentage points around the mean discrepancy. (text)

- Selected summary statistics from Table 1 (Absolute value of ratio of UVI to PI: summary measures of the absolute value of the discrepancy [(UV/PI)-1]):
  - Month-on-month (Germany Import): Mean 0.011; Standard deviation 0.010; Maximum 0.073; Root mean squared error 0.014; Mean absolute deviation 0.011.
  - Month-on-month (Japan Export): Mean 0.013; Standard deviation 0.010; Maximum 0.055; Root mean squared error 0.016; Mean absolute deviation 0.013.
  - Month-on-12 month (Germany Import): Mean 0.018; Standard deviation 0.016; Maximum 0.096; Root mean squared error 0.024; Mean absolute deviation 0.018.
  - Month-on-12 month (Japan Export): Mean 0.025; Standard deviation 0.019; Maximum 0.099; Root mean squared error 0.031; Mean absolute deviation 0.025.

- Table 2 (UVI and PI: percentage of changes of same and different sign), selected entries (Month-on-month):
  - Exports (Germany): same sign both positive 41.7; both negative 16.6; different signs UV positive : PI negative 12.5; UV negative : PI positive 29.2.
  - Imports (Japan): same sign both positive 41.8; both negative 21.3; different signs UV positive : PI negative 11.1; UV negative : PI positive 16.8.
- Table 5 (Terms of trade indices: discrepancy between UVIs and PIs):
  - Month-on-month (Germany): Mean 0.013; Standard deviation 0.010; Maximum 0.070; Root mean squared error 0.016.
  - Month-on-12 month (Japan): Mean 0.037; Standard deviation 0.027; Maximum 0.183; Root mean squared error 0.046.

- Table 10 (Comparison of deflated exports and imports by UVIs and PIs), selected entries:
  - Germany Exports (Billion Euros at constant 1999 prices): Unit values 591.5 (1999) to 799.0 (2005), Percentage change 35.1; Price indices 591.5 (1999) to 857.9 (2005), Percentage change 45.0.
  - Germany Imports (Billion Euros at constant 1999 prices): Unit values 796.3 (1999) to 785.5 (2005), Percentage change -1.4; Price indices 796.3 (1999) to 705.2 (2005), Percentage change -11.4.
  - Japan Exports (Billion at constant 1999 prices): Unit values 1,144.0 (1999) to 650.9 (2005), Percentage change -43.2; Price indices 1,144.0 (1999) to 674.1 (2005), Percentage change -41.0.
  - Japan Imports (Billion at constant 1999 prices): Unit values 4,957.0 (1999) to 4,353.9 (2005), Percentage change -16.3; Price indices 4,957.0 (1999) to 2,574.6 (2005), Percentage change -19.1.

### Identified sources and mechanisms of UVI bias
- Non-comparability of "like with like": UVIs suffer mainly from not comparing the prices of like with like, whereas establishment-based PIs do. (Section VI)
- Aggregation and stratification issues:
  - United Nations (1981) emphasized stratifying unit values by country of destination and size of batch; absence of highly detailed stratification criteria precludes benchmarking what is a reliable UVI. (Section VB)
  - Empirical studies with fine-grained scanner or brand/model/store-week stratifications (Bradley (2006); Silver and Webb (2002); Haan and Opperdoes (1999)) show substantial differences when aggregating unit values with and without such stratification, indicating unit value bias even at fine levels. (Section VB)
- Deletions/outlier routines:
  - Deletion routines commonly used to remove extreme unit value outliers can remove signal (large, irregular price changes) as well as noise, biasing UVIs toward undue stability. (Section VF)
  - Alterman (1991) estimated U.S. UVIs in 1985 were calculated for only 56 percent of the value of imports and 46 percent of the value of exports; for capital goods imports and exports were 30.3 and 26.1 percent respectively—illustrating extensive deletion/coverage loss. (Section VF)
- Formula differences:
  - PIs and UVIs may use different second-stage aggregation formulas (Laspeyres, Paasche, Fisher, chained indices), producing formula-driven differences; example for Germany: import price indices are Laspeyres referring to year 2000; national accounts deflators are annually chained Paasche indices; unit value indices are Paasche indices referring to year 2000. (Section VD)
  - Empirical illustration for Germany 2000–2005: UVI displayed a decline of 1.8% pa, the import price index increased slightly +0.3, and the import deflator decreased -0.8; geometric average of import price deflator and import price index gives estimate of -0.2% as the “true” annual change in import prices, implying the German UVI is significantly distorted downwards. (Section VD)
- Data environment changes and limits:
  - Customs/monetary unions may reduce documentation of intra-union trade, making customs data unsuitable; services and e-commerce growth make merchandise-based customs data increasingly incomplete for trade measurement. Establishment-based sources become the only practical option in many cases. (Section VE)
- Representativity and coverage:
  - PIs are designed to be representative via selected items and establishments; UVIs suffer from substantial discarding of outliers and coverage loss, raising concerns about representativity. (Section VI and VF)

### Predictive and cointegration evidence
- Predictive ability (Table 4): UVI predictive regressions show mixed F-statistics and p-values; PIs often Granger-cause UVIs strongly (e.g., Table 4: F-statistic PI GC UVI entries include 9.133, 5.969, 17.505, 18.258, 27.304, 19.824, 57.566, 62.057 with p-values 0.000.00…), indicating PI→UVI causality in many cases; UVIs rarely Granger-cause PIs (Table 4: F-statistic UVI GC PI entries include 0.339, 2.491, 2.571, 0.781, 0.405, 0.573, 113.486, 3.160 with some p-values significant only in limited cases). (Table 4)
- Unit root and cointegration tests (Table 3 and Table 7): tests frequently reject unit roots for monthly changes but cointegration between UVIs and PIs is generally absent or weak (E-G cointegration test statistics reported across series; many p-values not supportive of cointegration). (Tables 3 and 7)

### Practical implications and policy recommendations
- Primary recommendation: commence as soon as possible a program of establishment-based survey price collection to compile trade price indices (PIs). Establishment-based PIs compare like with like and are designed for representative coverage. (Section VI, VG)
- Avoid overreliance on UVIs as a cheaper alternative: the paper argues that advocating UVIs as the cheaper substitute is a disservice given their demonstrated deficiencies. (Section VI, VG)
- Hybrid strategies using UVIs where feasible are unproductive and can be misleading; reliance on UVIs should be minimized. (Section VA summary)
- Improve UVI quality only where feasible via more detailed stratification of customs data (country of origin/destination, size of batch, establishment identifiers, time strata such as week of purchase), but recognize practical limitations and lack of benchmarks for adequate stratification. (Section VB)
- Use other-country or global product price series as temporary proxies in select product areas where global price-taking assumptions are plausible, but view this as not a panacea. (Section VC)
- Be cautious about deletion routines: review outlier detection to avoid deleting substantive price changes (signal) that PIs would capture. (Section VF)
- Account for formula differences: where possible, harmonize index formulas or assess formula-driven biases when comparing UVIs and PIs (Laspeyres vs Paasche vs Fisher vs chained indices). (Section VD)
- Recognize resource constraints: countries with limited resources should prioritize development of establishment-based surveys as part of broader price-index systems; trade PIs are a logical extension of PPIs and offer more reliable measurement for policy. (Section VG)

### Selected product-group evidence on lower discrepancy groups
- Table 11 lists CPA 4-digit classes with the least month-on-month discrepancy (examples):
  - Manufacture of motor vehicles CPA-3410: Mean 0.0197; Maximum 0.0601; Minimum 0.0009; Standard deviation 0.0153.
  - Manufacture of pulp CPA-2111: Mean 0.0197; Maximum 0.0664; Minimum 0.0003; Standard deviation 0.0148.
  - Manufacture of motor vehicles parts and accessories CPA-3430: Mean 0.0260; Maximum 0.1266; Minimum 0.0001; Standard deviation 0.0212.
  - (Additional CPA classes and their statistics are reported in Table 11.)

### Concluding assessment
- The paper concludes that UVIs do not stand up to PIs designed to overcome their major failings: UVIs do not reliably measure export and import price inflation, nor terms of trade, nor do they reliably support deflation for volume measures of trade or national income. Establishment-based price indices are recommended despite higher resource requirements because they better measure major economic flows and support appropriate policy responses. (Section VI)

*Source: _wp07121 - 1.5 and 2 percent—at best still significant potential to mislead economists.*

### 0.025 to under 0.05325231

### _wp07121 - 0.025 to under 0.05325231

### Summary statistics and reported ranges
- Ranges reported:
  - 0.025 to under 0.05325231
  - 0.05 to under 0.07519177
  - 0.075 top under 0.18103
  - 0.1 to under 0.15332
  - 0.15 to under 0.2130
  - 0.0 to under 0.3121
- Single scalar appearing: 7710067
- Means (three values presented contiguously): 0.0530.0540.041
- Standard deviation (three values presented contiguously): 0.0340.0410.030
- Minimum (three values presented contiguously): 0.0150.0160.019
- Maximum (three values presented contiguously): 0.2030.2470.213
- Standard deviation of UV/PI ratio — Mean (three values): 0.0690.0730.059
- Standard deviation of UV/PI ratio — Standard deviation (three values): 0.0460.0580.075
- Standard deviation of UV/PI ratio — Minimum (three values): 0.0190.0220.024
- Standard deviation of UV/PI ratio — Maximum (three values): 0.2850.3230.594
- Page numbering indicated: 30, 31, 32, 33

### Appendix — Derivation of test of long-run differences between UVIs and PIs and TOT indices
- Setup:
  - Two price series p_t and P_t for t = 0,1,...,T with both price series starting at unity in period 0:
    - (1) p_0 = P_0 ≡ 1.
  - If one series grows at different rates compared to the other series:
    - (2) p_t = α_1 α_2 ... α_t P_t ;                                                                                               t = 1,...,T
    - α_t is one plus the differential rate of growth between the two series going from period t−1 to period t.
  - Implication:
    - (3) p_t/p_{t−1} = α_t (P_t/P_{t−1}) ;                                                                                         t = 1,...,T.
- Logarithmic rates of growth definitions:
  - (4) y_t ≡ ln(p_t/p_{t−1}) ; Y_t ≡ ln(P_t/P_{t−1}) ;                                                                       t = 1,...,T.
- Difference series and stochastic model:
  - Taking logarithms and rearranging yields:
    - (5) Z_t ≡ y_t − Y_t = β_t ;                                                                                                t = 1,...,T
    - (6) β_t ≡ ln α_t ;                                                                                                          t = 1,...,T.
  - Convert exact equations (5) into a simple stochastic model:
    - (7) Z_t = β + ε_t ;                                                                                                       t = 1,...,T
    - ε_t are independently distributed normal variables with mean 0 and constant variance.
  - Estimation:
    - The least squares and maximum likelihood estimator for β is the average of the Z_t which equals the average of the logarithmic growth rates of the p_t series (average of the y_t) less the average of the logarithmic growth rates of the P_t series (average of the Y_t).
- Hypothesis of interest:
  - (8) β = 0
  - Corresponds to:
    - (9) α = 1.
  - If (8) or (9) is accepted, the two measures of price change give the same answer in the long run.
- Extension to terms of trade (TOT):
  - Let unit value measures of export and import prices in period t be P_X^t and P_M^t respectively and let the price index measures be p_X^t and p_M^t respectively. Repeat above algebra for export and import prices.
  - Define logarithmic rates of growth of the terms of trade:
    - (10) y_{TT t} ≡ ln[(p_X^t/p_M^t)/(p_X^{t−1}/p_M^{t−1})] ; Y_{TT t} ≡ ln[(P_X^t/P_M^t)/(P_X^{t−1}/P_M^{t−1})];             t = 1,...,T.
  - Terms of trade regression counterpart:
    - (11) Z_{TT t} ≡ y_{TT t} − Y_{TT t} = β_{TT} + ε_{TT t} ;                                                                     t = 1,...,T.
  - Interpretation:
    - The two sets of price indexes give the same answer with respect to measuring changes in the terms of trade if β_{TT} equals 0.
    - The least squares or maximum likelihood estimator for β_{TT} is the average of the y_{TT t} less the average of the Y_{TT t}.
    - It can also be shown that this estimator, β_{TT}*, is equal to β_X* less β_M* where β_X* and β_M* are the estimators for β_X and β_M defined above.

*Source: _wp07121 - 0.025 to under 0.05325231 (PDF chapter/section).*

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