## _wp10133

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---

### I. Introduction and Summary Findings
- The Norwegian real effective exchange rate (CPI-based) has been broadly stable over the last 30 years, with a modest appreciation trend in the most recent decade.
- By the end of 2009, the real value of the krone was about 7 percent above its 30-year average.
- Main measurement finding:
  - The traditional CPI-based REER may understate Norway’s relative price appreciation by about 7-15 percentage points during 2000–2008.
  - About half of this difference can be attributed to increased trade with low-cost developing economies.
  - The other half stems from accounting for Norway’s low measured share of services compared to other advanced economies.

### II. Limitations of CPI-based REER and Motivation for Alternatives
- Key conceptual limitations of CPI-based bilateral real exchange rates:
  - CPI measures do not provide information about relative price levels between partners.
  - CPIs often do not properly account for differences in consumption baskets across countries.
  - Composition of CPIs often differs from composition of actual individual consumption within a country.
  - Actual consumption patterns differ across countries; CPIs and PCE deflators exclude costs of individual consumption borne by government.
- Empirical context and implications for Norway:
  - 2005 ICP PPP estimates suggest Norway is about four times as expensive as emerging market countries such as China and Russia, and nearly 40 percent more expensive than the average OECD economy.
  - Since 2000, the share of trade with developing countries has nearly doubled to over one quarter of mainland GDP.
  - The share of non-energy exports to developing countries increased from 10 percent to nearly 25 percent from 1990 to 2008.
  - Imports from developing countries increased from about 10 percent to nearly 25 percent of total imports from 1990 to 2008.
  - Large compositional shifts toward low-price partners can raise Norway’s trade-weighted relative price level by double digits even when bilateral real exchange rates do not change.
- Illustration (numerical example from source):
  - If initial trade weights are 90 percent with A and 10 percent with E, with bilateral relative price levels 1 vis-à-vis A and 4 vis-à-vis E, shifting to 80 percent with A and 20 percent with E (bilateral prices unchanged) raises the trade-weighted price level by nearly 14 percent while a conventional REER records no change.

### III. Incomparability of Underlying CPIs and Norway-specific Evidence
- CPI vs. AIC / PCE:
  - Personal Consumption Expenditure (PCE) deflators track actual individual consumption expenditure by households quarter to quarter; PCE includes some spending on behalf of consumers by employers and government agencies and includes substitution effects.
  - Actual Individual Consumption (AIC) includes goods and services paid for by individuals as well as services paid for by governments for the purpose of individual consumption (mostly education and health services); AIC is preferred to household consumption in international comparisons because government provision varies across countries.
- CPI weights and government-provided services:
  - Cumulative CPI weight on healthcare and education equals 3% in Norway, compared with 9% in Italy, 10% in the United States, and 15% in Switzerland.
  - As a share of actual individual consumption, services account for slightly over 50 percent in Norway—about the average of its partners.
  - In Norway and other Nordics, the general government accounts for nearly 40 percent of actual individual consumption of services.
- Housing rents and owner-occupied housing: methodologies vary greatly; Eurostat’s HICP excludes owner-occupied housing.
- Empirical patterns:
  - Growth in the relative costs of services in Norway has been far larger than in its partners since 2000.
  - The average cost of services is 1.4 times higher in Norway than the average of its industrialized partners.
  - Growth in the costs of publicly provided individual services appears to have outpaced growth in costs of private services by a total of 20 percent since 2000.
- Consequence:
  - Norwegian CPI likely understates the rise in the total costs of individual consumption because a large part of individual services are government-provided and underweighted in CPI.
  - Differences in CPI definitions and consumption baskets drive a wedge between the CPI non-traded share and the actual non-traded share in individual consumption.

### IV. Alternative Trade-weighted Measures Proposed
- Two trade-weighted measures of international relative prices for Norway:
  - Import average relative price (M_Q):
    - Aggregates bilateral relative prices across Norway’s trading partners using geographic composition of import trade volumes.
    - Bilateral form uses Norway’s consumption basket in numerator and partner’s prices in denominator, adjusted by nominal exchange rate E.
  - Export average relative price (X_Q):
    - Aggregates bilateral relative prices across Norway’s trading partners using geographic weights of non-energy export volumes.
    - Bilateral form uses partner’s consumption basket in numerator and Norway’s prices in denominator, adjusted by nominal exchange rate E.
  - The Fisher price index extension: Fisher index computed as the geometric average of the two Laspeyres/Paasche style bilateral indices.
- Interpretation notes:
  - If countries have similar consumption patterns, M_Q and X_Q should be similar.
  - If tradable goods prices are equalized internationally, deviations of M_Q and X_Q from unity reflect divergence in prices of non-traded goods.
  - Rising M_Q and X_Q can be associated with rising costs of non-traded goods domestically and possible loss of competitiveness if non-traded goods are inputs to exported tradables.
- Additional constructed measure Q_REER:
  - Uses PPP-implied bilateral relative prices from 2005 ICP extended using CPI-based bilateral RER developments and aggregated with Norway’s total non-energy trade weights to isolate interactions not captured by CPI-based REER.

### V. Data, Construction Methodology, and Coverage
- Benchmark and data:
  - Key benchmark source: International Comparison Program (ICP) 2005 survey.
  - ICP provides prices of comparable items, expenditure weights, real individual expenditure per capita (in international dollars) and price level indices; disaggregation limited to twelve COICOP categories.
  - ICP price indices rebased relative to the United States for consistency.
- Recursive extension:
  - Uses log-differenced decompositions to extend bilateral relative price levels backward and forward from the ICP 2005 benchmark; each decomposition includes nominal personal consumption expenditure growth (Norway and partner), bilateral nominal depreciation of the krone, and growth in real personal expenditure and prices across twelve expenditure categories.
  - Weights are updated recursively.
- Coverage:
  - Bilateral relative prices computed for Norway’s 23 major trading partners (covering ~80 percent of total non-petroleum exports and ~80 percent of total imports).
  - Aggregation to world averages uses volume-based import and export trade weights.
- Coverage caveat:
  - Cumulative weight of emerging markets in sample ≈ 15 percent in 2008, while actual trade shares appear to be in the mid 20s; given trade evolution since 2000, some 5 to 15 percentage point rise in international relative prices may remain unaccounted for.

### VI. Main Quantitative Results and Comparisons
- Divergence after 2000 (cumulative appreciation since 2000):
  - X_Q: 26 percent
  - M_Q: 20 percent
  - REER (CPI-based): 12 percent
  - Q_REER increased by about 7 percentage points relative to the REER over the same period.
- Interpretation:
  - Indicators M_Q, X_Q, and Q_REER move closely with CPI-based REER through the 1990s, diverging after 2000, indicating costs of living in Norway relative to trading partners rose more than the CPI-based REER suggests.
  - Trade-weighted relative price measures help close the gap between unit-labor costs and CPI-based REER which widened in recent years.
  - Increased trade with China identified as a major source of world average relative price changes.
  - Import relative price changes concentrated after 2000; 1990s were broadly neutral as increased trade with emerging markets offset declining bilateral prices and krone depreciation.
  - After 2000, shifting trade accompanied by generally rising Norwegian relative prices—Norway became more expensive relative to many industrialized partners (notably Sweden, the United States, Japan).
  - Export relative prices also driven by increased exports to emerging markets in the last decade; Norway’s bilateral prices appreciated strongly vis-à-vis many partners (United States, Sweden, United Kingdom).

### VII. Appendix: Regression Analysis on Equilibrium Determinants (1990–2008)
- Approach:
  - Trade-weighted relative price estimates regressed on commonly used determinants of equilibrium real effective exchange rates.
  - Annual measures converted to quarterly series by incorporating CPI-based bilateral RER quarterly dynamics.
  - Data expressed in logarithms covering 1990 to 2008.
- Estimated equation (preserved notation):
  - (6) Q* = α1*(TNTT - TNTT*) + α2*PPP** + α3*Oil + α4*NFA - α5*Interest + ε
- Determinants considered:
  - Productivity differentials (relative prices of non-traded vs. traded goods).
  - Real oil price (index of U.S. dollar brent price relative to the U.S. CPI).
  - Norway’s net foreign asset (NFA) position as a share of mainland GDP.
  - Relative cost of public services (differential between costs of publicly and privately provided individual services).
  - Interest differential (nominal short-term money market rate differential between Norway and key industrialized partners).
- Key coefficient estimates and statistics (from Table 3; standard errors in parentheses; significance markers preserved):
  - Productivity differential:
    - Qx: 0.581 *** (0.135)
    - Sqrt(Qx*Qm): 0.289 * (0.148)
    - Qm: 0.298 ** (0.127)
    - REER: 0.434 *** (0.14)
  - Oil price:
    - Qx: 0.047 *** (0.017)
    - Sqrt(Qx*Qm): 0.041 ** (0.018)
    - Qm: 0.042 ** (0.016)
    - REER: 0.045 ** (0.017)
  - Net foreign assets position:
    - Qx: 0.113 *** (0.031)
    - Sqrt(Qx*Qm): 0.109 *** (0.032)
    - Qm: 0.062 ** (0.028)
    - REER: 0.110 *** (0.031)
  - Relative cost of public services:
    - Qx: 0.218 (0.266)
    - Sqrt(Qx*Qm): 0.227 (0.282)
    - Qm: -0.113 (0.247)
    - REER: 0.228 (0.271)
  - Interest differential:
    - Qx: 0.036 (0.239)
    - Sqrt(Qx*Qm): 0.071 (0.256)
    - Qm: 0.478 (0.223)
    - REER: 0.052 (0.245)
  - Constant:
    - Qx: -0.106 (0.272)
    - Sqrt(Qx*Qm): -0.124 (0.285)
    - Qm: 4.524 (0.251)
    - REER: -0.123 (0.275)
  - R ²:
    - Qx: 0.862
    - Sqrt(Qx*Qm): 0.805
    - Qm: 0.655
    - REER: 0.838
- Interpretation highlights:
  - Interest rate differential is insignificant in these specifications; possible reason: use of short-term rates rather than long-term rates.
  - NFA coefficients imply a rise in NFA of 10 percent of mainland GDP is associated with a 1 percent increase in relative prices.
  - Doubling of real oil prices would lead to a 5 percent rise in relative prices (based on coefficient interpretation).
  - The geometric average Sqrt(Qx*Qm) is considered to account for substitution effects under homothetic and identical preferences across partners.
  - Qx and Qm provide a better fit for developments in equilibrium real exchange rate fundamentals; R squareds for Qx and Qm are substantially higher than for the REER in some specifications.
  - The significance of the oil price variable disappears when the sample period excludes 2007 and/or 2008.

### VIII. Policy-relevant Implications
- Because a large part of Norway’s individual services are provided by government and underweighted in the CPI, Norwegian CPI generally understates increases in the total costs of individual consumption.
- Mismeasurement by CPI-based REERs implies conventional competitiveness measures may understate Norway’s relative price appreciation, particularly since 2000, with implications for policy assessment of competitiveness and external adjustment.

*Source: _wp10133 — IMF staff calculations and analysis contained in the paper.*

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

### _wp10133 - References

### I. INTRODUCTION
- The Norwegian real effective exchange rate (CPI-based) has been broadly stable over the last 30 years, with a modest appreciation trend in the most recent decade.
- By the end of 2009, the real value of the krone was about 7 percent above its 30-year average.
- CPI-based REER measures are practical (computationally easy and timely) but do not:
  - Provide information about relative price levels between partners.
  - Properly account for differences in consumption baskets across countries.
- Two key limitations identified:
  - Dispersion of bilateral relative price levels among trading partners is substantial.
  - Cross-country differences in consumption patterns (both CPI composition and actual individual consumption) are substantial. Example: the weight of services in Norway’s CPI is relatively small due to public provision of services such as healthcare and education.
- New measures constructed in the paper:
  - Are relative price levels rather than index numbers.
  - Account for dispersion in bilateral relative price levels, allowing trade-composition shifts (e.g., toward low-cost partners) to generate dynamics in trade-weighted relative prices.
  - Adjust for cross-country differences in baskets and actual consumption patterns.
- Main quantitative statement on measurement differences:
  - The traditional CPI-based REER may understate Norway’s relative price appreciation by about 7-15 percentage points during 2000–2008.
  - About half of this difference can be attributed to increased trade with low-cost developing economies.
  - The other half stems from accounting for Norway’s low measured share of services compared to other advanced economies.

### II. ALTERNATIVES TO THE CPI-BASED REER
#### A. Why REER Mismeasures Changes in International Relative Prices
- Problem: REER computations aggregate CPI changes across partners into an index number; traditionally rely on fixed trade weights but even time-varying weights can miss shifts toward low-cost producers if bilateral real exchange rates do not change.
- Illustrative numerical example:
  - Country N initial trade weights: 90 percent with country A (Advanced) and 10 percent with country E (Emerging).
  - Bilateral relative price levels: 1 vis-à-vis A and 4 vis-à-vis E.
  - If trade shares shift to 80 percent with A and 20 percent with E while bilateral prices remain unchanged, the REER records no change, but the trade-weighted price level rises by nearly 14 percent.
- Empirical context for Norway:
  - Norway is among the most expensive countries globally (Big Mac Index, UBS city rankings).
  - 2005 ICP PPP estimates suggest Norway is about four times as expensive as emerging market countries such as China and Russia, and nearly 40 percent more expensive than the average OECD economy.
  - PPP surveys are infrequent: conducted every six years and available with a two year lag.
  - Since 2000, the share of trade with developing countries has nearly doubled to over one quarter of mainland GDP.
  - The share of non-energy exports to developing countries increased from 10 percent to nearly 25 percent from 1990 to 2008.
  - Imports from developing countries increased from about 10 percent to nearly 25 percent of total imports from 1990 to 2008.
  - Much of this compositional adjustment has occurred since 1999.
- Implication:
  - Large compositional shifts toward countries with significantly lower price levels can translate into double-digit increases in Norway’s trade-weighted relative price level even when bilateral real exchange rates do not change.

*Source: _wp10133 - References*

### 2. Incomparability of the underlying Consumer Price Indexes

### 2. Incomparability of the underlying Consumer Price Indexes

### Key problems with CPI-based bilateral real exchange rates
- CPI-based real exchange rates tend to misspecify changes in the relative costs of living for two main reasons:
  - Composition of CPIs often differs from composition of actual individual consumption within a country.
  - Actual consumption patterns differ across countries.
- CPIs and PCE deflators:
  - Personal Consumption Expenditure (PCE) deflators track actual individual consumption expenditure by households from quarter to quarter, are broader in scope, and include some spending on behalf of consumers by employers and government agencies; they include substitution effects due to changes in relative prices.
  - Actual Individual Consumption (AIC) consists of goods and services paid for by individuals as well as services paid for by governments for the purpose of individual consumption (mostly education and health services); AIC is preferred to household consumption in international comparisons because the amount of individual services provided by government varies across countries.
- CPIs and government-provided individual consumption:
  - Both CPI and PCE deflator measure out-of-pocket consumption expenditures by households and thus exclude the costs of actual individual consumption borne by the government.
  - Example: cumulative CPI weight on healthcare and education equals 3% in Norway, compared with 9% in Italy, 10% in the United States, and 15% in Switzerland.
- Housing rents and owner-occupied housing:
  - Methodologies for imputing costs of owner–occupied housing vary greatly; inclusion/exclusion affects short-term CPI movements significantly.
  - Eurostat’s HICP excludes owner-occupied housing from its scope.

### Illustration: how differing CPI weights distort bilateral comparisons
- Example 2 (from source):
  - Assume shares of goods and services each equal to 50 percent of actual individual consumption in both country N and country A.
  - CPI weights differ: weight on goods is 60 percent in country N's CPI and 40 percent in country A's CPI.
  - If prices of goods rise by 10 percent and prices of services by 30 percent in both countries:
    - CPI rises by 18 percent in country N and 22 percent in country A.
    - Cost of total individual consumption rises by 20 percent in both countries.
- Balassa-Samuelson effect noted: productivity grows faster in tradable sector than in nontradables, leading to faster growth of prices of non-tradables; services (non-traded goods) are relatively more expensive in richer countries.

### Norway-specific evidence on services and government provision
- Relative costs and consumption pattern facts (2005 / 1990–2008 references in text and figures):
  - The growth in the relative costs of services in Norway has been far larger than in its partners since 2000.
  - The average cost of services is 1.4 times higher in Norway than the average of its industrialized partners (source note: Average vis-à-vis industrialized countries = 1.4).
  - As a share of actual individual consumption, services account for slightly over 50 percent in Norway—about the average of its partners.
  - In Norway and other Nordics, the general government accounts for nearly 40 percent of actual individual consumption of services (Figure 6).
  - Consumption volumes: privately and publicly provided individual services grew at a similar pace throughout the last two decades (Figure 7).
  - Price/costs: growth in the costs of publicly provided individual services appears to have outpaced the growth in the costs of private services by a total of 20 percent since 2000 (Figure 8).
- Implication: Norwegian CPI likely understates the rise in the total costs of individual consumption because a large part of individual services are government-provided and thus underweighted in CPI.

### Consequence: wedge between CPI non-traded share and actual individual consumption
- Differences in CPI definitions and consumption baskets drive a wedge between:
  - The share of non-traded goods recorded in the CPI, and
  - The actual share of non-traded goods in individual consumption.
- When services (non-tradables) rise faster, personal cost indices understate true rises in total individual consumption costs.

---

### Alternative measures proposed
- Goal: mitigate shortcomings of the REER that arise from CPI composition and international consumption-basket differences.
- Two trade-weighted measures of international relative prices for Norway:
  - Import average relative price (M_Q):
    - Defined by aggregating bilateral relative prices across Norway’s trading partners using geographic composition of import trade volumes.
    - Bilateral form: uses Norway’s consumption basket in numerator and partner’s prices in denominator, adjusted by nominal exchange rate E (krone per foreign currency units).
    - Notation (as in source): M_Q = Σ Σ E · yp_N / yp_P · Q (source presents equation (2) in original notation).
  - Export average relative price (X_Q):
    - Defined by aggregating bilateral relative prices across Norway’s trading partners using geographic weights of non-energy export volumes.
    - Bilateral form: uses partner’s consumption basket in numerator and Norway’s prices in denominator, adjusted by nominal exchange rate E.
    - Notation (as in source): X_Q = Σ Σ E · yp_P / yp_N · Q (source presents equation (3) in original notation).
- Relationship and interpretation:
  - The only difference between the bilateral measures is the choice of consumption basket.
  - If countries have similar consumption patterns, M_Q and X_Q should be similar.
  - XM_Q Q ≤ (textual source statement: XMQQ) — intuition: including optimal basket in denominator vs numerator leads to inequality.
  - If tradable goods prices are equalized internationally, deviations of M_Q and X_Q from unity reflect divergence in prices of non-traded goods.
  - Rising M_Q and X_Q can be associated with rising costs of non-traded goods domestically, and possibly with loss of competitiveness if non-traded goods serve as inputs to exported tradables.

- Extension: Fisher price index
  - A natural extension is to compute a Fisher price index as the geometric average of the two Laspeyres/Paasche style bilateral indices (import and export measures).

---

### Construction methodology (data and recursive extension)
- Benchmark and data:
  - Key benchmark source: International Comparison Program (ICP) 2005 survey.
  - ICP provides: prices of comparable items and expenditure weights; real individual expenditure per capita (in international dollars) and price level indices.
  - Disaggregation limited to twelve personal consumption expenditure categories (COICOP).
  - Adjustment: ICP price indices rebased relative to the United States to ensure consistency between product of real expenditures and price index with nominal expenditures.
- Recursive extension beyond benchmark:
  - Use log-differenced decompositions to extend bilateral relative price levels backward and forward (equations (4) and (5) in the source):
    - Each equation decomposes ΔQ into terms for nominal personal consumption expenditure growth (Norway and partner), bilateral nominal depreciation of the krone, and growth in real personal expenditure and prices across twelve expenditure categories.
  - Starting point: ICP benchmark year (2005) where real expenditure weights and relative prices are used to compute growth rates for adjacent years; weights updated recursively.
- Coverage:
  - Bilateral relative prices computed for Norway’s 23 major trading partners (covering ~80 percent of total non-petroleum exports and ~80 percent of total imports).
  - Aggregation to world averages uses volume-based import and export trade weights.
- Additional measure Q_REER:
  - Constructed to resemble Thomas et al (2008) WARP: PPP-implied bilateral relative prices from 2005 ICP are extended using CPI-based bilateral RER developments and aggregated using Norway’s total non-energy trade weights.
  - Q_REER isolates interaction between relative price levels and trade weights not captured by CPI-based REER.

---

### Relative price estimates and main quantitative findings
- Comparison to CPI-based REER:
  - Indicators (M_Q, X_Q, Q_REER) move closely with CPI-based REER through 1990s, diverge after 2000.
  - Cumulative appreciation since 2000:
    - X_Q: 26 percent
    - M_Q: 20 percent
    - REER (CPI-based): 12 percent
  - Q_REER increased by about 7 percentage points relative to the REER over the same period.
- Coverage caveat and possible understatement:
  - Cumulative weight of emerging markets in sample ≈ 15 percent in 2008, while actual trade shares appear to be in the mid 20s; given trade evolution since 2000, some 5 to 15 percentage point rise in international relative prices may remain unaccounted for.
- Relationship to other indicators:
  - Trade-weighted relative price measures help close gap between unit-labor costs and CPI-based REER which widened in recent years.
  - Improvement in Norway’s non-oil terms of trade supported a sizable rise in relative labor costs unmatched by consumer prices.
  - Higher share of services in the relative price measures (whose costs rose more than traded goods) contributes to this reconciliation, along with increased trade with developing countries exporting cheap consumer goods.
- Contributions to changes (summary from Tables 1 and 2 in source):
  - Increased trade with China is identified as a major source of world average relative price changes.
  - Import relative price changes mostly occurred after 2000; 1990s showed broadly neutral strengthening as increased trade with emerging markets offset declining bilateral prices and krone depreciation.
  - After 2000, shifting trade accompanied by generally rising Norwegian relative prices—Norway became more expensive relative to many industrialized partners (notably Sweden, the United States, Japan).
  - Export relative prices also driven by increased exports to emerging markets in the last decade; Norway’s bilateral prices appreciated strongly vis-à-vis many partners (United States, Sweden, United Kingdom).

---

### Summary (source conclusions)
- Two new trade-weighted measures of international relative prices for Norway were derived.
- Developments in these measures followed CPI-based REER in the 1990s but diverged after 2000, indicating that costs of living in Norway relative to trading partners rose more than the CPI-based REER suggests.
- Both sources of potential mismeasurement contributed:
  - Largest factor: rapidly rising share of developing countries among Norway’s trade partners.
  - Second factor: inconsistent definitions of consumption baskets across partner economies, which causes the REER to understate Norway’s appreciation when service prices rise fast.
- Policy-relevant implication: because a large part of Norway’s individual services are provided by government and therefore underweighted in CPI, Norwegian CPI generally understates increases in the total costs of individual consumption.

*Source: _wp10133 - 2. Incomparability of the underlying Consumer Price Indexes*

### References

### References

### Bibliographic references
- Akram Q.F., 2002, “PPP in the medium run despite oil shocks: The case of Norway,” Working Paper 2002/4, Norges Bank.
- Akram Q.F., 2003, “Real equilibrium exchange rates for Norway,” Chapter 4 in this issue of Norges Bank Occasional Papers.
- Balassa B., 1964, “The purchasing power doctrine: A reappraisal,” Journal of Political Economy 72, 584–596.
- Bjørnland H.C. and Hungnes H., 2002, “Fundamental determinants of the long run real exchange rate: The case of Norway,” Discussion Paper 326, Statistics Norway.
- Canzoneri M.B., Cumby R.E., Diba B., 1999, “Relative labor productivity and the real exchange rate in the long run: Evidence for a panel of OECD countries,” Journal of International Economics 47, 245 – 266.
- Cashin P. P.R., Ce ́spedes L.F. and Sahay R., 2004, “Commodity currencies and the real exchange rate,” Journal of Development Economics 75, 239 – 268.
- Christensen A. K., Dupont J., Schreyer P., 2005, “International comparability of the consumer price index: owner-occupied housing”, Paper prepared for the OECD seminar “Inflation measures: too high – to low – internationally comparable?,” Paris, June 2005.
- Chaudhury K. and Daniel B.C., 1998, “Long-run equilibrium real exchange rates and oil prices,” Economic Letters 58, 231–238.
- Deaton A. and Heston A., 2009, “Understanding PPPs and PPP-based national accounts,” November 2009.
- Gershenkron A., 1947, “The Soviet indices of industrial production,” Review of Economic Studies, 29(4), 217–26.
- Habib M. M. and Kalamova M. M., 2007, “Are there oil currencies? The real exchange rate of oil exporting countries,” Working Paper 839/2007, European Central Bank.
- Johannessen R., 2004, “Owner-occupied housing in Norway: Why the rental equivalence approach is preferred,” Paper presented at the Eight Meeting of International Working Group on Price Indices, Helsinki, August 2004.
- Lane P.R. and Milesi-Ferretti G.M., 2002, “External wealth, the trade balance, and the real exchange rate,” European Economic Review 46, 1049 – 1071.
- Neary, J. P., 2004, “Rationalizing the Penn World Table: True multilateral indexes for international comparisons of real income,” American Economic Review 94, 1411–1428.
- Rogoff K., 1996, “The purchasing power parity puzzle,” Journal of Economic Literature 34, 647–668.
- Samuelson P., 1964, “Theoretical notes on trade problems,” Review of Economics and Statistics 46, 145–154.
- Strauss J. and Ferris M.E., 1996, “The role of nontraded and traded wages in the productivity differential model,” Southern Economic Journal 63, 327 – 338.
- The Economist, 1992 – 2009, The Big Mac Index.
- Thomas C.P, Marquez J., and Fahle S., 2008, “Measuring U.S. international relative prices: a WARP view of the world,” International Finance Discussion Papers 917, January, Board of Governors of the Federal Reserve System.
- UBS, 2009, A comparison of purchasing power around the globe: Prices and earnings 2009.
- World Bank, 2008, Global purchasing power parities and real expenditures: 2005 international comparison program.
- World Bank, 2007, ICP 2003–2006 Handbook. Washington, DC., http://www.worldbank.org/data/icp

### Table excerpt: Norway's major trading partners (In percent of total volume)
- Belgium: 1990 1.6, 2008 2.3; 1990 2.3, 2008 1.7
- Finland: 1990 2.9, 2008 2.4; 1990 3.3, 2008 3.7
- France: 1990 5.5, 2008 4.5; 1990 3.8, 2008 3.8
- Germany: 1990 11.8, 2008 10.1; 1990 14.4, 2008 14.9
- Ireland: 1990 0.3, 2008 0.7; 1990 0.9, 2008 1.1
- Italy: 1990 4.1, 2008 2.9; 1990 3.4, 2008 3.5
- Netherlands: 1990 5.1, 2008 7.5; 1990 4.0, 2008 4.1
- Portugal: 1990 1.2, 2008 1.2; 1990 1.1, 2008 0.3
- Spain: 1990 1.5, 2008 3.0; 1990 1.1, 2008 2.2
- Canada: 1990 0.7, 2008 0.5; 1990 2.3, 2008 2.7
- Denmark: 1990 5.9, 2008 5.7; 1990 6.7, 2008 6.1
- Japan: 1990 3.0, 2008 2.7; 1990 4.6, 2008 2.6
- Korea, Rep.: 1990 0.4, 2008 3.7; 1990 0.5, 2008 1.4
- Singapore: 1990 1.1, 2008 2.6; 1990 0.5, 2008 0.4
- Sweden: 1990 13.3, 2008 9.9; 1990 15.2, 2008 12.9
- Switzerland: 1990 1.3, 2008 0.7; 1990 1.6, 2008 1.2
- United Kingdom: 1990 10.3, 2008 6.5; 1990 8.1, 2008 5.6
- United States: 1990 6.4, 2008 6.1; 1990 8.2, 2008 5.9
- India: 1990 0.1, 2008 1.1; 1990 0.2, 2008 0.4
- China: 1990 0.4, 2008 3.8; 1990 0.7, 2008 7.0
- Brazil: 1990 0.5, 2008 1.1; 1990 0.5, 2008 1.2
- Total: 1990 77.6, 2008 78.9; 1990 83.1, 2008 82.6

### Appendix 1 and Appendix 2 — Explaining International Relative Prices

### Rationale and approach
- The appendix investigates Norway’s international relative prices with respect to established equilibrium exchange rate fundamentals.
- Trade-weighted relative price estimates are regressed on commonly used determinants of equilibrium real effective exchange rates.
- Annual measures are converted into quarterly series by incorporating CPI-based bilateral real exchange rate quarterly dynamics.
- Data are expressed in logarithms and cover the period from 1990 to 2008.
- Determinants considered (based on existing studies for Norway, e.g., Akram, 2003; Bjørnland et al., 2002):
  - Productivity differentials: Measured as the difference between relative prices of non-traded goods (services) and traded goods. Measured as Norwegian differential relative to foreign differential; trade-weighted foreign differential aggregates changes in relative prices.
  - Real oil price: Measured as the index of U.S. dollar brent price relative to the U.S. CPI.
  - Norway’s net foreign asset (NFA) position: Measured as a share of mainland GDP.
  - Relative cost of public services: Measured as the differential between the costs of publicly and privately provided individual services.
  - Interest differential: Nominal interest rate differential between Norway and its key industrialized partners on short term money market instruments.

### Estimated equation
- The estimated equation (6) is:
  (6) Q* = α1*(TNTT - TNTT*) + α2*PPP** + α3*Oil + α4*NFA - α5*Interest + ε
  (Note: equation text preserved as presented in the source.)

### Key empirical findings (from Table 3)
- Sample: 1990Q1-2008Q4.
- Notes: *, **, and *** indicate 10, 5, and 1 percent statistical significance respectively.
- Main coefficient estimates and standard errors (by dependent variable columns Qx, Sqrt(Qx*Qm), Qm, REER):
  - Productivity differential:
    - Qx: 0.581 *** (0.135)
    - Sqrt(Qx*Qm): 0.289 * (0.148)
    - Qm: 0.298 ** (0.127)
    - REER: 0.434 *** (0.14)
  - Oil price:
    - Qx: 0.047 *** (0.017)
    - Sqrt(Qx*Qm): 0.041 ** (0.018)
    - Qm: 0.042 ** (0.016)
    - REER: 0.045 ** (0.017)
  - Net foreign assets position:
    - Qx: 0.113 *** (0.031)
    - Sqrt(Qx*Qm): 0.109 *** (0.032)
    - Qm: 0.062 ** (0.028)
    - REER: 0.110 *** (0.031)
  - Relative cost of public services:
    - Qx: 0.218 (0.266)
    - Sqrt(Qx*Qm): 0.227 (0.282)
    - Qm: -0.113 (0.247)
    - REER: 0.228 (0.271)
  - Interest differential:
    - Qx: 0.036 (0.239)
    - Sqrt(Qx*Qm): 0.071 (0.256)
    - Qm: 0.478 (0.223)
    - REER: 0.052 (0.245)
  - Constant:
    - Qx: -0.106 (0.272)
    - Sqrt(Qx*Qm): -0.124 (0.285)
    - Qm: 4.524 (0.251)
    - REER: -0.123 (0.275)
  - R ²:
    - Qx: 0.862
    - Sqrt(Qx*Qm): 0.805
    - Qm: 0.655
    - REER: 0.838

### Interpretation and notable points
- Interest rate differential is found to be insignificant in contrast to previous studies; one potential reason is the use of short-term rates rather than long-term rates.
- Productivity differential coefficient values vary across specifications; the REER coefficient is slightly above the 0.23 estimate obtained for Norway or 0.19 found for cross-country studies.
- NFA coefficients suggest that a rise in NFA of 10 percent of mainland GDP is associated with a 1 percent increase in relative prices.
- Doubling of real oil prices would lead to a 5 percent rise in the relative prices (based on coefficient interpretation).
- The significance of the oil price variable disappears when the sample period excludes 2007 and/or 2008.
- The geometric average of export and import relative prices (Sqrt(Qx*Qm)) is considered as a measure that would account for substitution effects under homothetic and identical preferences across partners.
- The Qx and Qm measures provide a better fit for developments in equilibrium real exchange rate fundamentals; R squared for both Qm and Qx equations are substantially higher than for the REER.

*Source: IMF staff calculations.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10133.pdf_