## _wp0457

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---

### I. Purpose, context, and empirical evaluation strategy
- Purpose:
  - Assess slack in the Finnish economy via the output gap to gauge inflationary pressures and to distinguish cyclical from potential growth variations.
- Evaluation strategy:
  - Intuitive criteria: gap mean ~ zero over long horizons; reasonable maxima/minima; ability to capture known episodes (late 1980s overheating, 1990–93 swing, late 1990s narrowing driven by recovery and ICT boom).
  - Econometric evaluation: simulated out-of-sample forecasting in a Phillips-curve framework linking inflation to slack; recursive estimation for 1960–2002 with real-time data up to 1990–2002 producing one-year-ahead predicted inflation compared to actual.

### II. Key descriptive findings on Finland’s business cycle (selected facts)
- Recent 15-year episode (1990s–2002) features:
  - Sharp recession early 1990s; real GDP growth averaging about 5 percent in 1994–2000 (ICT-led boom); significant slowdown later.
  - Unemployment rose from 3.2 percent in 1990 to 16.4 percent three years later; decreased to about 9.1 percent in 2001 and remained flat in 2002.
- Volatility:
  - Volatility discussed via coefficient of variation of quarterly growth rates; Finnish output described as pronouncedly volatile, partly ICT-driven.

### III. Statistical detrending / filtering results and sensitivities
- Arithmetic trends (LT, QT, ET):
  - All identify early 1990s trough with estimated gap in excess of 10 percent of GDP.
  - QT: average positive gap between 1980 and 2002 amounts to 3.0 percent of potential GDP.
  - ET: indicates real GDP did not pass potential in the 1990s boom.
  - Arithmetic trends produce extremes > 10 percent of potential GDP in both directions.
- Hodrick-Prescott (HP) filter (1980–2002; λ = 20, 50, 100, 200):
  - All HP variants: estimated gaps close to zero on average and agree on peak/trough dates, but magnitude sensitive to λ.
  - Example sensitivity:
    - Gap in trough year 1993 varies between approximately -5 percent and -9 percent of trend GDP across λ choices.
    - For λ = 100 (standard assumption): gap for the original series ending in 2002 is approximately zero (a closed gap).
    - For λ = 20 (less smooth trend): the gap using the original series = -1.6 percent of trend GDP.
  - Endpoint problem and forecast-extensions:
    - Extending series to 2005 using IMF WEO forecasts changes HP 2002 gap estimates materially.
    - For λ = 100:
      - Original series (sample end 2002): output gap ≈ closed (approximately zero).
      - Extended to 2005: output gap in 2002 is positive by 1.2 percent of trend.
    - For λ = 20:
      - Original series: gap = -1.6 percent of trend GDP.
      - Extended to 2005 and 2008: extensions indicate a positive output gap on the order of 0.3 percent of GDP.
    - Interpretation: trade-off between endpoint bias and reliance on out-of-sample forecast reliability; recommended sensitivity analysis with different growth scenarios.
- Beveridge-Nelson (BN) decomposition (ARIMA(1,1,1)):
  - BN trend closely tracks actual real GDP.
  - BN identifies early 1990s slump: maximum output gap in 1991 at about -7 percent of trend GDP.
  - BN: output gap positive one year in 1994; more consistently positive 1996–2000; slowdown in 2001 detected.

### IV. Frequency-domain (FD) filter and band-pass findings
- Method:
  - Band-pass targeting business cycle periodicity between 2 and 8 years (annual data 1960–2002); Corbae and Ouliaris (2002) approach for nonstationary data avoids loss of observations at ends.
- FD results (1980–2002 summary):
  - Average output gap close to zero.
  - Overheating late 1980s: positive gap reaching 5 percent of potential GDP (FD peak later specified as 5.1 percent in 1990).
  - Trough in 1993: gap reaches -3.5 percent of potential output.
  - Gap closed rapidly after 1993; marginally positive 1995–2000.
  - Negative gap in 2001–2002, reaching -1.4 percent of GDP in 2002.
  - FD reports a deep trough between 1984 and 1988 comparable to early 1990s trough — unique to this filter.
- FD vs BN timing/magnitudes:
  - FD peak: 5.1 percent in 1990; BN peak: 1.3 percent one year earlier.
  - FD trough: -3.5 percent in 1993; BN trough: -6.4 percent two years earlier.

### V. Theory-based measures: Blanchard-Quah (BQ) and Production Function (PF)
- Blanchard-Quah (BQ) decomposition (VAR with log GDP and unemployment):
  - BQ identifies supply (permanent) vs demand (transitory) shocks.
  - BQ indicates output markedly above potential in 1985–1990 (starting several years earlier than most measures).
  - Crisis trough in early 1990s: about -8 percent of potential GDP in 1993.
  - BQ gap remains negative until end of sample (2002) — suggests late 1990s strong growth was largely supply-driven (high potential growth), consistent with muted inflationary pressures.
- Production Function (PF) approach (Cobb-Douglas; tfp = y - αk - (1-α)l):
  - Potential labor ∗Lt = LFt (1 - ∗tUR) with time-varying NAWRU estimated via Kalman filter.
  - NAWRU estimates:
    - Trend unemployment highest in 1996 at approximately 14.7 percent.
    - Estimated NAWRU in 2002: 8.3 percent.
    - Official unemployment rate in 2002: 9.1 percent.
  - PF output gap results (1963–2002):
    - Mean output gap: 0.2 percent on average per year between 1980 and 2002.
    - Peak/trough symmetry: gap of approximately 6.4 percent of trend GDP associated with peak in 1989 and trough in 1993.
    - Gap closed by 1997; positive during 1997–2001; slipped negative in 2002 — negative 2002 gap aligns with other economic indicators.
  - ICT / TFP contributions (growth accounting):
    - During 1994–2000 boom, TFP contributed on average 3.5 percentage points to actual growth — almost double combined capital and labor contribution.
    - ICT contribution volatile: less than 2 percentage points (1999) to almost 5 percentage points (1997).
    - In 2001 ICT dip briefly negative; in 2002 capital and labor together contributed approx. 0.5 percentage points while TFP almost reached 1 percentage point.

### VI. Econometric forecast evaluation (output gaps in a Phillips-curve forecasting framework)
- Forecast design:
  - π_{t+1} - π_t = α + β L(π_t) + γ L(xt) + e_t with xt = output gap measure; one-year-ahead forecasts; annual data; recursive out-of-sample evaluation for 1990–2001 using estimation start 1960–1989.
  - HP real-time (one-sided) series constructed for λ = 20 and λ = 100.
- Root mean square error (RMSE 1/) and Theil's U 2/ (values preserved exactly):
  - RMSE 1/:
    - PF: 1.71
    - FD: 1.52
    - HP100(rt): 1.90
    - HP20(rt): 1.97
    - BQ: 1.18
    - HP100: 1.94
    - HP20: 2.12
    - no output gap: 1.14
  - Theil's U 2/:
    - PF: 1.11
    - FD: 0.99
    - HP100(rt): 1.24
    - HP20(rt): 1.29
    - BQ: 0.77
    - HP100: 1.27
    - HP20: 1.38
    - no output gap: 0.74
- Forecast performance conclusions:
  - BQ and, to a limited extent, FD produce forecasts better than the naïve "no change" forecast in Theil's U terms (Theil's U < 1).
  - The univariate AR model of inflation ("no output gap") outperforms FD and BQ by RMSE (RMSE 1.14 for no gap vs BQ 1.18 and FD 1.52).
  - HP variants and PF do not improve inflation forecasts relative to the univariate model in this sample.
  - Reasons for weak performance of gap measures: high output volatility, limited annual sample size; quarterly data may help but create measurement issues.

### VII. Cross-method comparison, uncertainty, and practical recommendations
- Cross-method dispersion:
  - Considerable uncertainty in level estimates; 2002 gap estimates vary between -1.5 percent and 1.2 percent of potential GDP across methods.
  - Standard deviations for HP, FD, BN, BQ, PF typically in the 2 to 4 percent range; arithmetic trends produce much larger extremes and standard deviations.
- Practical recommendations:
  - Production function approach attractive due to NAWRU derivation and explicit ICT–TFP link; further work should better incorporate long-run demographics and explicit treatment of the ICT sector.
  - Frequency-domain approach: business-cycle duration choice is crucial; further research to identify an "optimal" frequency recommended.
  - HP filter: despite level uncertainty, dynamics similar to PF and FD measures; HP could be reasonable for estimating changes in the gap if level uncertainty is acknowledged.
  - BQ measure produced the lowest RMSE in this sample; expanding VAR dimensionality might improve cyclical identification but would benefit from quarterly data given annual-sample limitations.
  - For HP endpoint issues: undertake sensitivity analysis using different growth scenarios for forecast extensions or use models that address nonstationarity (e.g., Beveridge-Nelson).

### VIII. Appendix summary — cointegration and NAWRU considerations
- Tests indicate wage inflation and unemployment are nonstationary; Johansen cointegration tests cannot reject the null r = 0 (no cointegration), supporting NAWRU approaches.
- VAR lag selection suggests three lags (levels) by Schwarz and Hannan-Quinn criteria.
- Consideration of structural breaks (early 1990s unemployment surge) and small-sample bias adjustments discussed; results remain broadly consistent with no cointegration.

*Source: _wp0457 — IMF staff working paper (selected content provided).*

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

### _wp0457 - References

### I. Introduction: purpose and relevance
- Assessing slack in the economy via the output gap is important for:
  - gauging inflationary pressures relative to potential output;
  - calculating the “structural fiscal balance” and gauging fiscal policy thrust;
  - assessing whether variations in actual growth are cyclical or reflect changes in potential growth.
- This paper explores primarily the first and, to a lesser extent, the third aspect in the Finnish context.

### Box 1 — Finland: Volatility in the Real Economy
- Recent 15-year episode features:
  - (1) one of the sharpest recessions among euro-area countries in the early 1990s;
  - (2) a strong boom in the second half of the 1990s—with real GDP growth averaging about 5 percent in 1994–2000, led by the information and communication technology (ICT) sector;
  - (3) a significant slowdown in economic growth later.
- Unemployment dynamics:
  - unemployment rate rose from 3.2 percent in 1990 to 16.4 percent three years later;
  - since 1993 unemployment decreased continuously until about 9.1 percent in 2001, and remained flat in 2002.
- Data and measurement notes:
  - volatility measured by the coefficient of variation of quarterly growth rates.
  - Real GDP growth: Finland vs. other euro area countries: Growth and Volatility figures provided (e.g., Finland 1.8/2.1; Euro area 3/2.3 with notes on exclusions).
  - Sources: IMF, International Financial Statistics (IFS) and World Economic Outlook (WEO) databases; data for 1990-2002.

### Unobservability and methodological overview
- The output gap = actual GDP minus unobservable potential output.
- Two broad methodological sets:
  - Statistical filters (time-domain and frequency-domain);
  - Model-based approaches (e.g., production function, structural decompositions).
- Evaluation strategy:
  - Intuitive criteria: gap mean ~ zero over long horizons; reasonable maxima/minima; capture stylized facts (late 1980s overheating, 1990–93 swing, late 1990s narrowing driven by recovery and ICT boom).
  - Econometric evaluation: simulated out-of-sample forecasting in a Phillips-curve framework linking inflation to slack; recursive estimation for 1960–2002 with real-time data up to 1990–2002 and one-year-ahead predicted inflation compared to actual.

### Key empirical evaluation result (forecasting)
- For 1960–2002, only the frequency domain filter and the Blanchard-Quah decomposition help forecasting CPI inflation relative to a naïve “no change” forecast.
- Both of these measures perform worse than a simple autoregressive model of inflation.
- Weak performance of output gap measures attributed to pronounced volatility of Finnish output, in part driven by the ICT sector.

### II. Review of the literature (summary)
- Two main approaches:
  - Statistical properties of GDP series (trend = potential output): methods include arithmetic detrending, Hodrick-Prescott (HP) filter, Beveridge-Nelson (BN), frequency domain methods (Corbae and Ouliaris (2002)).
  - Economic model–based potential output: accounting for underemployed resources (labor market), examples include Blanchard and Quah (1989), production function approaches (Artus (1977); De Masi (1997); Kuttner (1994); Denis, Mc Morrow, and Roeger (2002)).
- On Finland: relatively little comparative work; examples include Brunila, Hukkinen, and Tujula (1999); Gylfason (1998); Rasi and Viikari (1998).

### III. Measures of potential output and the output gap — Statistical measures
- Goal: decompose actual output into trend (potential) and cyclical component.
- Arithmetic trends:
  - Linear trend (LT), Quadratic trend (QT), Exponential trend (ET).
  - All identify the early 1990s trough with estimated gap in excess of 10 percent of GDP.
  - Differences:
    - LT: output gap turned positive in 1998 and remained so.
    - QT: gap closed only briefly in 2000; average positive gap between 1980 and 2002 amounts to 3.0 percent of potential GDP.
    - ET: indicates real GDP did not pass potential in the 1990s boom.
  - All arithmetic trends record extremes > 10 percent of potential GDP in both directions.
- Univariate statistical filters:
  - Time-domain: Hodrick-Prescott (HP), Beveridge-Nelson (BN).
  - Frequency-domain: Corbae and Ouliaris (2002) approach.

### The Hodrick-Prescott (HP) filter — properties and Finnish results
- HP filter formulation: penalizes second difference of trend; penalty parameter λ controls smoothness.
- Standard literature value: λ = 100 for annual data (used as base case).
- Known drawbacks:
  - possibility of spurious cyclicality for integrated series;
  - arbitrary choice of λ;
  - neglect of structural breaks and shifts;
  - end-of-sample bias due to symmetric two-sided filtering.
- Finnish-specific considerations:
  - real GDP likely integrated; structural breaks present; choice of λ affects whether ICT boom is seen as cyclical or trend.
- Empirical HP results (1980–2002) for λ = 20, 50, 100, and 200:
  - All estimated gaps are close to zero on average and agree on peak/trough dates.
  - Magnitude varies significantly: e.g., gap in trough year 1993 varies between approximately -5 percent and -9 percent of trend GDP across λ choices.
  - All HP filters indicate the gap was closed as early as 1997.
  - Estimates for the gap in 2002 vary widely:
    - smoothest trend (largest λ) indicates actual GDP was above trend by 1.1 percent of potential GDP;
    - the least smooth trend results in actual output being below trend (exact value not restated in provided text).

### III.B Model-based approaches (overview)
- Blanchard-Quah decomposition: explored as a model-based alternative and found useful in inflation forecasting.
- Production function approach:
  - avoids pure statistical separation but requires estimates of labor input at full employment, stock of effective capital input, and total factor productivity growth.
  - Finnish challenges: determining the extent of structural increases in unemployment vs. higher natural rate; possible obsolescence of capital stock after collapse of trade with Russia; importance of ICT-driven technological progress.

### IV. Structure of the remainder of the paper
- Section II: literature review.
- Section III: description of various output gap measures for Finland.
- Section IV: comparison of measures in a forecast model for Finnish CPI inflation.
- Section V: main results and conclusions.

*Source: _wp0457 - References (IMF staff working paper PDF content provided).*

### 1.6 percent below potential. The standard assumption of

### _wp0457 - 1.6 percent below potential. The standard assumption of

### Hodrick-Prescott (HP) detrending results for Finland (1980–2002)
- Figures compare Actual GDP and HP trends (in billions of euro, at 1995 prices) for λ = 20, 50, 100, 200; last observation of the original time series is 2002.
- Output gaps presented (in percent of trend) for λ = 20, 50, 100, 200 show substantial sensitivity to the smoothing parameter λ.
- For λ = 100 (standard assumption): gap for the original series ending in 2002 is approximately zero (a closed gap).
- For λ = 20 (less smooth trend): the gap using the original series is equal to -1.6 percent of trend GDP.

### HP filter endpoint problem and sensitivity to forecast extensions
- Adding forecasted values at the end of the observation period (using IMF’s WEO forecasts) until 2005 and until 2008 materially changes HP output gap estimates.
- For all parameter values, gap estimates based on the extended series are higher than for the original series.
- Specific numeric comparisons:
  - For λ = 100:
    - Original series (sample end 2002): output gap ≈ closed (approximately zero).
    - Extended to 2005 (using forecasts): output gap in 2002 is positive, indicating real GDP above potential by 1.2 percent of trend.
  - For λ = 20:
    - Original series (sample end 2002): gap = -1.6 percent of trend GDP.
    - Extended to 2005 and 2008: both extensions indicate a positive output gap on the order of 0.3 percent of GDP.
- Interpretation:
  - The HP estimation approach creates a trade-off between endpoint bias (using the original series) and reliance on out-of-sample forecast reliability (using extended series).
  - The negative output gap in 2002 from the original series was replaced—due to the specific forecasted path of GDP—by a closed gap that is less consistent with the general economic background of low inflation and slowly rising unemployment.
- Suggested practices:
  - Undertake a sensitivity analysis using different growth scenarios for the forecast period.
  - Alternatively, shift empirical focus to the nonstationary character of the underlying data and use models that treat nonstationarity more technically (e.g., Beveridge-Nelson decomposition).

### Beveridge-Nelson (BN) decomposition approach
- Conceptual approach:
  - Decomposes a nonstationary time series (real GDP) into a nonstationary trend and a cyclical component using Box-Jenkins (1976) ARIMA (p,d,q) modeling.
  - Assumes innovations in the permanent (trend) and transitory (cyclical) components are perfectly negatively correlated.
- Empirical implementation:
  - Based on inspection of the resulting trend component, an ARIMA(1,1,1) model is chosen to represent the structure of the underlying series (series assumed integrated of order one, d = 1).
- Results and interpretation:
  - The BN decomposition yields a trend that closely tracks actual real GDP.
  - The decomposition correctly identifies the early 1990s slump, with the maximum output gap reached in 1991 at about -7 percent of (trend) GDP.
  - According to the decomposition:
    - The output gap becomes positive for one year in 1994.
    - The output gap is more consistently positive between 1996 and 2000.
  - The growth slowdown in 2001 is detected by the decomposition.

*Source: IMF staff calculations and text from the provided content unit.*

### 5.6 percent in 2000 to 0.7 percent) translates into a swing of the output gap from almost

### _wp0457 - 5.6 percent in 2000 to 0.7 percent) translates into a swing of the output gap from almost

### Frequency Domain (FD) Filter: method and findings
- Approach:
  - Filters a stationary time series to eliminate fluctuations below or above specified frequencies; targets business cycle frequency based on Burns and Mitchell (1946) duration assumption of between 1.5 and 8 years.
  - Exact band-pass filter eliminates frequencies outside a range; time-domain approximations (Baxter and King (1999)) trade off approximation quality versus lost observations at sample ends.
  - Corbae and Ouliaris (2002) provide a consistent band-pass filter for nonstationary data in the frequency domain without loss of observations at either end.
- Results for Finland (1960–2002, annual data; business cycle periodicity assumed between two and eight years):
  - Average output gap over 1980–2002 is close to zero.
  - Overheating in late 1980s associated with a positive output gap reaching 5 percent of (potential) GDP (text later specifies 5.1 percent peak in 1990).
  - Trough in 1993: gap reaches -3.5 percent of potential output.
  - Gap closed rapidly after 1993, remained marginally positive over 1995–2000.
  - Negative output gap in 2001–2002, reaching -1.4 percent of GDP in 2002.
  - Notable deep trough between 1984 and 1988 comparable in depth to the early 1990s trough — a result unique to this filter.
- Comparison with Beveridge-Nelson (BN):
  - FD peak: 5.1 percent of trend GDP in 1990; BN peak: 1.3 percent reached one year earlier.
  - FD trough: -3.5 percent in 1993; BN trough: -6.4 percent occurring two years earlier.

### Theory-Based Measures: overview
- Methods discussed:
  - Blanchard-Quah (BQ) permanent-transitory decomposition: identifies supply shocks (permanent) versus demand shocks (temporary) in a VAR framework using (log) real GDP and the unemployment rate.
  - Production function (PF) approach: Cobb-Douglas form Yt = TFPt Kt^α Lt^β with α+β=1; potential output derived from trend TFP and potential labor consistent with a natural rate of unemployment.
- Trade-offs:
  - BQ: explicit economic foundations; potential output associated with cumulated supply shocks; gap identified as demand component; identification depends on suitability of the variable representing demand (unemployment rate).
  - PF: tractability and ability to account for sources of growth (labor, capital, TFP); reliance on filtered series (tfp*, NAWRU) introduces discretion; data requirements and parameter assumptions (constant factor shares) are important caveats.

### Blanchard-Quah (BQ) results for Finland
- Characteristics:
  - Output remained markedly above potential in 1985–1990 according to BQ (starting several years earlier than most measures).
  - Crisis trough in early 1990s: about -8 percent of potential GDP in 1993 (text: "about eight percent of potential GDP in 1993").
  - Unique feature: BQ output gap remains negative until end of sample (2002), implying strong growth in late 1990s was largely supply-driven (high potential growth), and inflationary pressures remained muted.

### Production Function (PF) approach: setup and Finland application
- Setup:
  - Cobb-Douglas production function with constant returns to scale; TFP derived as a residual: tfp = y - αk - (1-α)l (log form).
  - Potential labor ∗Lt = LFt (1 - ∗tUR) where ∗tUR is time-varying natural rate of unemployment.
  - Trend TFP (tfp*) smoothed (e.g., HP filter) and NAWRU estimated via Kalman filter in a bivariate model of unemployment and change in wage inflation.
- NAWRU estimation results:
  - Trend unemployment highest in 1996 at approximately 14.7 percent.
  - Estimated NAWRU in 2002: 8.3 percent.
  - Official unemployment rate in 2002: 9.1 percent.
  - Wage inflation modeled as ARMA(2,3) in the optimal structure.
- PF output gap results (1963–2002):
  - Mean output gap: 0.2 percent on average per year between 1980 and 2002.
  - Peak/trough symmetry: gap of approximately 6.4 percent of trend GDP associated with peak in 1989 and trough in 1993.
  - Gap closed by 1997, turned positive during 1997–2001, then slipped negative in 2002.
  - Negative gap in 2002 aligns with general economic indicators.
- ICT and growth accounting insights:
  - TFP surge associated with ICT sector significantly boosted potential growth in the late 1990s.
  - During the boom (approx. 1994–2000), TFP contributed on average 3.5 percentage points to actual growth—almost double the combined contribution of capital and labor.
  - ICT contribution was highly volatile: varied between less than 2 percentage points (1999) and almost 5 percentage points (1997).
  - In 2001 ICT contribution dipped briefly into negative territory; in 2002, capital and labor together contributed approximately 0.5 percentage points while TFP almost reached 1 percentage point.

### Econometric evaluation: output gaps and inflation forecasting
- Forecast framework:
  - Variant of Phillips curve: π_{t+1} - π_t = α + β L(π_t) + γ L(xt) + e_t where xt is an output gap measure; one-year-ahead inflation forecast; annual data; evaluation period 1990–2002.
  - Simulated out-of-sample recursive forecasting: model estimated on 1960–1989, then rolled forward annually to produce forecasts for 1990–2001.
  - HP real-time (HP..rt) constructed with λ = 20 and λ = 100 to create one-sided "real-time" series for evaluation.
- Table 1 key statistics (preserved exactly as presented):
  - RMSE 1/ (Root mean square error multiplied by 100):
    - PF: 1.71
    - FD: 1.52
    - HP100(rt): 1.90
    - HP20(rt): 1.97
    - BQ: 1.18
    - HP100: 1.94
    - HP20: 2.12
    - no output gap: 1.14
  - Theil's U 2/:
    - PF: 1.11
    - FD: 0.99
    - HP100(rt): 1.24
    - HP20(rt): 1.29
    - BQ: 0.77
    - HP100: 1.27
    - HP20: 1.38
    - no output gap: 0.74
  - Note: PF = production function; FD = frequency domain; HP100(rt) = real-time HP with λ=100; HP20(rt) = real-time HP with λ=20; BQ = Blanchard-Quah.
- Forecast performance findings:
  - Only BQ and, to a limited extent, FD produce forecasts better than the naïve "no change" forecast (Theil's U < 1).
  - The univariate autoregressive model of inflation ("no output gap") outperforms FD and BQ by RMSE.
  - HP real-time measures show RMSEs slightly smaller than ex-post two-sided HP measures, but neither HP variants nor PF improve inflation forecasts relative to the univariate model.
  - Possible reasons for disappointing performance of gap measures:
    - High volatility of output complicates accurate estimation of potential output.
    - Annual data limits observations; quarterly data could help but introduces other issues (capital stock intra-year measurement, seasonality).
  - Beveridge-Nelson (BN) omitted from econometric evaluation due to initialization observation loss.

### Summary of descriptive results and concluding remarks
- Cross-method differences:
  - Significant differences across methods, e.g., 2002 gap estimates vary between -1.5 percent and 1.2 percent of potential GDP.
  - Considerable uncertainty about the size of Finland's output gap.
- Descriptive statistics (Table 2 highlights; values preserved where quoted in text):
  - Many measures’ averages close to zero; exceptions: quadratic trend, exponential trend, Blanchard-Quah (BQ).
  - Arithmetic filters (linear, quadratic, exponential) produce exceptionally large extremes and high standard deviations, reducing attractiveness.
  - Remaining measures (HP, FD, BN, BQ, PF) display standard deviations in the range of 2 to 4 percent.
- Practical implications and recommendations for further work:
  - Production function approach attractive because of NAWRU derivation and explicit ICT–TFP link; future refinements should better incorporate long-run demographics and the ICT sector explicitly (e.g., Jalava and Pohjola (2001)).
  - Frequency domain approach: definition of business cycle duration is crucial; further research to identify an "optimal" frequency recommended.
  - HP filter: despite level uncertainty, dynamics are fairly similar to PF and FD measures; could be a reasonable method to estimate changes in the gap even if levels are uncertain.
  - The BQ measure produced the lowest RMSE in this sample; larger VARs could potentially improve cyclical identification but would benefit from quarterly data given the limited annual-sample observations.

### Appendix — Is there a long-run Phillips curve in Finland?
- Tests and findings:
  - Both wage inflation and unemployment are nonstationary, but tests show no sign of cointegration between them — result conducive to NAWRU approach.
  - VAR lag selection by Schwarz and Hannan-Quinn criteria proposes three lags (in levels).
  - Likelihood ratio tests indicate both series appear nonstationary; unemployment can be considered weakly exogenous.
  - Johansen cointegration tests: null r = 0 (no cointegrating relationship) cannot be rejected at conventional levels.
  - Considerations:
    - Possible structural break (sharp unemployment rise early 1990s) was explored; dummies did not soften evidence against cointegration.
    - Small sample bias corrections (e.g., Cheung and Lai (1993)) would raise critical values and make noncointegration easier to accept.
- Visual and test supplements:
  - Figure A1 presents price inflation (CPI), wage inflation (economy-wide average wage), unemployment rate (percent of labor force), and real GDP growth for 1980–2002 (percent change over previous year unless noted).
  - Cointegration test statistics (L-max and Trace) reproduced in the Appendix indicate inability to reject r = 0.

*Source: IMF, IFS; and IMF staff calculations.*

### REFERENCES

### REFERENCES

### Methods for measuring potential output and output gaps
- Apel, M. and P. Jansson, 1997, “System Estimates of Potential Output and the NAIRU,” Sveriges Riksbank Working Paper No. 41 (Stockholm: Sveriges Riksbank).
- Artus, J.R., 1977, “Measures of Potential Output in Manufacturing for Eight Industrial Countries, 1955–78,” Staff Papers, International Monetary Fund, 24, 1–35.
- De Masi, P.R., 1997, “IMF Estimates of Potential Output: Theory and Practice,” IMF Working Paper 97/177 (Washington, DC: International Monetary Fund).
- Denis, C., K. Mc Morrow and W. Roeger, 2002, “Production function approach to calculating potential growth and output gaps—estimates for the EU Member States and the US,” European Commission Economic Papers, No. 176 (Brussels: European Commission).
- Kuttner, K.N., 1994, “Estimating Potential Output as a Latent Variable,” Journal of Business & Economic Statistics, 12, 361–8.
- Ross, K. and A. Ubide, 2001, “Mind the Gap: What is the Best Measure of Slack in the Euro Area?” IMF Working Paper 01/203 (Washington, DC: International Monetary Fund).
- Scacciavillani, F. and P. Swagel, 1999, “Measures of Potential Output: An Application to Israel,” IMF working paper 99/96 (Washington, DC: International Monetary Fund).

### Filters, detrending, and business-cycle extraction
- Baxter, M and R. King, 1999, “Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series,” Review of Economics and Statistics, 81, 575–93.
- Beveridge, S. and C.R. Nelson, 1981, “A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the ‘Business Cycle’,” Journal of Monetary Economics, 7, 151–74.
- Canova, F., 1999, “Does Detrending Matter for the Determination of the Reference Cycles and Selection of Turning Points,” Economic Journal, 109, 126–50.
- Harvey, A.C. and A. Jaeger, 1993, “Detrending, Stylized Facts and the Business Cycle,” Journal of Applied Econometrics, 8, 231–47.
- Hodrick, R.J. and E.C. Prescott, 1997, “Post-War U.S. Business Cycles: An Empirical Investigation,” Journal of Money, Credit, and Banking, 29, 1–16.
- Ravn, M.O., and H. Uhlig, 2002, “On Adjusting the Hodrick-Prescott Filter for the Frequency of Observations,” Review of Economics and Statistics, 84(2), 371–80.
- Corbae, D. and S. Ouliaris, 2002, “Extracting Cycles from Non-Stationary Data,” (unpublished; Austin, Texas and Singapore: University of Texas and National University of Singapore).
- ————, and P.C.B. Phillips, 2002, “Band Spectral Regression with Trending Data,” Econometrica, 70, 1067–109.

### NAIRU, labor market, and slack measures
- Benes, J. and P. N’Diaye, 2004, “A Multivariate Filter for Measuring Potential Output and the NAIRU: Application to the Czech Republic,” IMF Working Paper 04/45 (Washington, DC: International Monetary Fund).
- Berger, H. and A. Billmeier, 2003, “Estimating the Output Gap in Finland” in Finland: Selected Issues, IMF Country Report 03/326 (Washington, DC: International Monetary Fund).
- Brunila, A., J. Hukkinen, and M. Tujula, 1999, “Indicators of the Cyclically Adjusted Balance: The Bank of Finland’s Experience,” Bank of Finland Discussion Paper 1/99 (Helsinki: Bank of Finland).
- Gylfason, T., 1998, “Unemployment, Efficiency, and Economic Growth: The Case of Finland,” Ekonomiska Samfundets Tidskrift, 3, 193–203.
- Rasi, C-M. and J-M. Viikari, 1998, “The Time-Varying NAIRU and Potential Output in Finland,” Bank of Finland Discussion Paper No. 6/98 (Helsinki: Bank of Finland).
- Schreiber, S. and J. Wolters, 2003, “What’s Wrong with the (German) NAIRU?” (unpublished; Berlin and Frankfurt: Free University Berlin and University of Frankfurt).

### Country applications, case studies, and IMF reports
- Billmeier, A., 2004, “Ghostbusting: Which Output Gap Measure Really Matters?” forthcoming as IMF Working Paper (Washington, DC: International Monetary Fund).
- De Masi, P.R., 1997, “IMF Estimates of Potential Output: Theory and Practice,” IMF Working Paper 97/177 (Washington, DC: International Monetary Fund).
- Everaert, L. and F. Nadal De Simone, 2003, “Capital Operating Time and Total Factor Productivity,” IMF Working Paper 03/128 (Washington, DC: International Monetary Fund).
- IMF (International Monetary Fund), 2003, “Finland: Staff Report for the 2003 Article IV Consultation,” IMF Country Staff Report No. 03/325 (Washington, DC: International Monetary Fund).
- Jalava, J. and M. Pohjola, 2001, “Economic Growth in the New Economy,” World Institute for Development Economics Research Discussion Paper No. 2001/5 (Helsinki: United Nations University).
- Wagner, N., 2001, “A Note on Finland’s New Economy” in Finland: Selected Issues, IMF Country Staff Report No. 01/215 (Washington: International Monetary Fund).
- Scacciavillani, F. and P. Swagel, 1999, “Measures of Potential Output: An Application to Israel,” IMF working paper 99/96 (Washington, DC: International Monetary Fund).

### Time series econometrics, forecasting, and related theory
- Blanchard, O. and D. Quah, 1989, “The Dynamic Effects of Aggregate Demand and Supply Disturbances,” American Economic Review, 79, 655–73.
- Box, G.E.P. and G.M. Jenkins, 1976, Time Series Analysis, Forecasting and Control (San Francisco: Holden Day).
- Burns, A.F. and W.C. Mitchell, 1946, Measuring Business Cycles (New York: National Bureau of Economic Research).
- Cheung, Y.-W., and K.S. Lai, 1993, “Finite Sample Sizes of Johansen’s Likelihood Ratio Tests for Cointegration,” Oxford Bulletin of Economics and Statistics, 55, 313–28.
- Johansen, S., 1995, Likelihood based Inference on Cointegration in the Vector Autoregressive Model (Oxford: Oxford University Press).
- Kuttner, K.N., 1994, “Estimating Potential Output as a Latent Variable,” Journal of Business & Economic Statistics, 12, 361–8.
- Orphanides, A. and S. van Norden, 2003, “The Reliability of Inflation Forecasts Based on Output Gap Estimates in Real Time,” CIRANO Scientific Series Working Paper 2003s-01 (Montreal: Centre Interuniversitaire de Recherché en Analyse des Organizations).
- Robinson, T., A. Stone, and M. van Zyl, 2003, “The Real-Time Forecasting Performance of Phillips Curves,” Reserve Bank of Australia Research Discussion Paper 2003-12 (Sidney: Reserve Bank of Australia).
- Stock, J.H. and M.W. Watson, 1999, “Forecasting Inflation”, Journal of Monetary Economics, 44, 293–335.
- Theil, H., 1971, Principles of Econometrics (New York: Wiley).
- Planas, C. and A. Rossi, 2003, “Program GAP – Version 2.2, Technical Appendix” (unpublished; Ispra, Italy: European Commission, Joint Research Centre).

*Source: _wp0457 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp0457.pdf_