## _wp1310

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---

### Principal conclusions and key findings
- Okun’s Law is a strong and stable relationship in most countries; deviations occur but are usually modest in size and short-lived.
- Data are consistent with traditional models in which fluctuations in unemployment are caused by shifts in aggregate demand.
- Okun coefficient examples:
  - Japan: –0.15
  - United States: –0.45 (example)
  - Spain: –0.85
- Cross-country coefficient differences reflect national labor-market features (e.g., Japan’s tradition of lifetime employment; prevalence of temporary contracts in Spain).
- Within a given country, the Okun coefficient is relatively stable over time; the coefficient generally does not show a systematic rise over time.

### Conceptual framework and equations
- Long-run concepts:
  - Potential output: Yt*
  - Natural rate of unemployment: Ut*
- Underlying relationships:
  - (1) Et – Et* = γ (Yt – Yt*) + ηt, γ > 0
  - (2) Ut – Ut* = δ (Et – Et*) + μt, δ < 0
  - Derived Okun’s Law:
    - (3) Ut – Ut* = β (Yt – Yt*) + εt, β < 0, where β = γδ and εt = μt + δηt
- Changes specification:
  - (4) ΔUt = α + β ΔYt + ωt
- Interpretation notes:
  - β depends on γ (employment response to output) and δ (unemployment response to employment).
  - γ expected to be less than 1.5.
  - δ expected to be less than one in absolute value.
  - Good fit of Okun’s Law implies εt is usually small.

### Estimation approaches and methodological notes
- Two primary approaches:
  - Levels equation (3): requires estimation of Ut* and Yt* (typically via HP filter).
  - Changes equation (4): uses ΔUt and ΔYt and implicitly assumes constant Ut* and constant growth of Yt*.
- HP smoothing parameters:
  - Annual: λ = 100 and λ = 1,000
  - Quarterly: λ = 1,600 and λ = 16,000
- Quarterly specifications often include two lags of output gap.
- Robustness checks: alternative Ut* and Yt* constructions (e.g., fixing end-of-sample Ut* and growth of Yt* at 2007 values; forecast-error approaches; CBO estimates).

### United States — empirical results (annual and quarterly)
- Broad annual result:
  - U.S. Okun’s Law coefficient typically around –0.4 or –0.5, with an R-squared in the neighborhood of 0.8.
- Annual estimates (1948–2011):
  - Levels, HP λ = 100: β = -0.411*** (0.024); Obs 64; Adjusted R^2 0.817; RMSE 0.426
  - Levels, HP λ = 1,000: β = -0.383*** (0.023); Obs 64; Adjusted R^2 0.813; RMSE 0.524
  - First differences: β = -0.405*** (0.029); α = 1.349*** (0.116); Obs 63; Adjusted R^2 0.752; RMSE 0.556
- Tests for nonlinearities and time variation:
  - Example (λ = 100): positive gaps coefficient = –0.37 and negative gaps coefficient = –0.39; p-value for equality = 0.61.
  - sup-Wald maximal F statistics = 5.30, 3.99, and 4.49 for baseline specs (λ = 100, λ = 1,000, and changes), below 10 percent critical value 7.12.
  - Sample-halves (1948-1979 vs 1980-2011) for levels (λ = 100): –0.35 and –0.41; p-value for equality = 0.20.
  - Decade-by-decade equality cannot be rejected (p-value = 0.38).
- Endpoint/HP-filter notes:
  - With HP λ = 100, estimated Ut* rises from about 5 percent in the early 2000s to 8.7 percent in 2011.
  - Growth rate of Yt* over 2008-2011 (HP λ = 100) is 1.3 percent.
  - Alternative 2007 fixed values: Ut* in 2007 = 4.9 percent; growth rate of Yt* (change 2006–2007) = 2.8 percent.
  - Using alternative end-of-sample Ut* and Yt* produces regression coefficient –0.40 (close to baseline –0.41).
- Forecast-error approach (Survey of Professional Forecasters, Q1 forecasts 1971–2011):
  - Regression of four-quarter forecast error in unemployment on four-quarter forecast error in output: Coefficient = –0.32 (standard error = 0.03); R2 = 0.68.
  - For same sample, regression of actual four-quarter change in Ut on actual change in Yt: Coefficient = –0.37 (standard error = 0.04).
- CBO-based estimates (1980–2011, using CBO Ut* and Yt*):
  - Estimated Okun coefficient = –0.55; R2 = 0.89.
  - Note: CBO estimates embed a version of Okun’s Law in the macro model (not independent evidence).

### Quarterly estimation results (United States)
- Levels specification (no lags):
  - Coefficients = –0.43 and –0.41 (for λ = 1,600 and λ = 16,000 respectively).
- Levels with two lags:
  - Current-term coefficients smaller; two lags significant.
  - Sums of current and lagged coefficients = –0.49 and –0.45.
  - R2 = 0.87 for λ = 1,600 with lags.
- Changes specification (quarterly):
  - No lags: coefficient on ΔY = –0.29; R2 = 0.49.
  - With lags: sum of coefficients = –0.43; R2 = 0.66.
  - Quarterly changes specification is somewhat noisier than levels or annual changes.
- Replication/update of Okun (1962) (quarterly):
  - Okun’s original quarterly no-lags coefficient ≈ –0.30; authors’ longer-sample no-lags coefficient ≈ –0.29.
  - Including two lags yields sums of coefficients –0.44 (Okun’s sample) and –0.43 (full sample), indicating lag structure explains much of the difference.

### Output → Employment → Unemployment (system/SUR estimates, annual 1948-2011)
- Joint SUR estimates with HP λ = 100:
  - E_t – E_t* = γ (Y_t – Y_t*) + η_t: γ = 0.543*** (0.040); Obs 64; Adjusted R^2 0.610
  - U_t – U_t* = δ (E_t – E_t*) + μ_t: δ = -0.728*** (0.027); Obs 64; Adjusted R^2 0.798
  - U_t – U_t* = β (Y_t – Y_t*) + ε_t: β = -0.405*** (0.024); Obs 64; Adjusted R^2 0.820
  - Test H0: β = γδ fails to be rejected (p-value = 0.378).

### International evidence and cross-country estimates (20 advanced economies, annual 1980-2011)
- Sample: 20 countries (OECD members in 1985, population > one million).
- Overall fit:
  - R^2 exceeds 0.4 in all countries but Austria and Italy.
  - Spain: R^2 = 0.90 (highest).
  - Japan: R^2 = 0.74; coefficient –0.16.
- Selected country β estimates (HP λ = 100, 1980-2011):
  - Australia: β = -0.536*** ( 0.0476); Obs 32; Adjusted R^2 0.797; RMSE 0.439
  - Austria: β = -0.136*** ( 0.0438); Obs 32; Adjusted R^2 0.213; RMSE 0.375
  - Canada: β = -0.432*** ( 0.0374); Obs 32; Adjusted R^2 0.805; RMSE 0.495
  - Japan: β = -0.152*** ( 0.0194); Obs 32; Adjusted R^2 0.654; RMSE 0.229
  - Spain: β = -0.852*** ( 0.0503); Obs 32; Adjusted R^2 0.899; RMSE 0.757
  - United States: β = -0.454*** ( 0.0373); Obs 32; Adjusted R^2 0.821; RMSE 0.418
- Robustness/averages across specifications:
  - Averaging across 20 countries:
    - R^2 = 0.63 for λ = 100 results.
    - R^2 = 0.59 for λ = 1,000.
    - R^2 = 0.49 for the changes equation.
    - Average coefficients: –0.40, –0.37, and –0.33 for the three specifications respectively.
- Stability over time:
  - Split 1980-1995 vs 1996-2011: seven of 20 countries reject equality at five percent level; in five of those seven cases the coefficient is lower in absolute value in the second half.
  - Average coefficient across 20 countries: –0.43 (first half) and –0.36 (second half).
  - Correlation of coefficients across periods = 0.49.
  - Overall, data do not support the view that Okun coefficient has generally risen over time.

### The Great Recession and “jobless recoveries”
- Evidence:
  - Apparent breakdowns of Okun’s Law during the Great Recession largely disappear once cross-country differences in coefficients and recession lengths are accounted for.
  - Authors find no evidence of a structural breakdown in Okun’s Law for the United States.
- Quantitative summary for U.S. 2009–2011:
  - Output gap averaged –10.8 percent.
  - Unemployment gap averaged 4.4 percentage points.
  - Ratio of the two gaps = –0.41 (close to earlier Okun estimates).
- Cross-country peak-to-trough analysis:
  - Nineteen of 20 countries experienced a recession beginning in late 2007 or 2008.
  - Simple change-in-output vs change-in-unemployment regression yields R^2 = –0.03 (no correlation).
  - Correcting for recession length T: cumulative regression without constant gives α = 0.70 (standard error = 0.30) and β = –0.12 (standard error = 0.25); R^2 = 0.54.
  - Allowing country-specific α_i and β_i (using annual Okun estimates, α_i/4 for quarterly fit): α_i average = 0.87 (0.22 once divided by four); fitted equation yields R^2 = 0.76.
  - Spain’s large rise in unemployment explained by large β_i combined with recession length.
- Germany:
  - Predicted change in unemployment for Germany: 2.2 percentage points.
  - Actual change in unemployment for Germany: –0.3 percentage points.
  - Residual modest relative to cross-country differences; “miracle” is an exaggeration.

### Attempts to explain cross-country coefficient differences
- Exploratory analysis in Section VII finds limited success in explaining cross-country differences.
- Candidate predictors tested include average unemployment and OECD EPL index; no robust general predictor found.
- Country-specific narratives:
  - Spain (β = –0.85): high incidence of temporary contracts (~one-third of employment) increases ease of employment adjustment.
  - Japan (β = –0.16): tradition of lifetime employment reduces layoffs; coefficient increased modestly over time but remains low.
  - Switzerland (β = –0.24): large use of foreign workers leads to employment changes being accommodated by labor-force movements; decomposition shows E–Y coefficient = 0.46 and U–E coefficient = –0.17.
  - Austria (β = –0.14): both E–Y and U–E coefficients implausibly small (< 0.02); no explanation offered.

### Overall assessment and conclusion
- Okun’s Law is a robust macroeconomic relationship: strong and stable by macroeconomic standards, though parameters differ across advanced economies.
- Reports of deviations are often exaggerated; Okun’s Law is more reliable than many macro relationships such as the Phillips curve.
- Evidence is consistent with models where aggregate demand shifts cause short-run unemployment fluctuations; other theories are not ruled out.
- Puzzle remains: Okun coefficient is far smaller than implied by an inverted production function; traditional explanation invokes costs of adjusting employment. The question whether small Okun coefficients arise naturally in alternative unemployment models is left for future research.

*Source: Excerpt from IMF working paper content (_wp1310).*

### 1980. Our principal conclusion is that Okun’s Law is a strong and stable relationship in most

### _wp1310 - 1980. Our principal conclusion is that Okun’s Law is a strong and stable relationship in most

### Principal conclusions and key findings
- Okun’s Law is a strong and stable relationship in most countries; deviations occur but are usually modest in size and short-lived.
- Data are consistent with traditional models in which fluctuations in unemployment are caused by shifts in aggregate demand.
- The Okun coefficient (the effect of a one-percent change in output on the unemployment rate) varies across countries:
  - Japan: –0.15
  - United States: –0.45 (example)
  - Spain: –0.85
- Cross-country coefficient differences reflect national labor-market features (e.g., Japan’s tradition of lifetime employment; prevalence of temporary contracts in Spain).
- Within a given country, the Okun coefficient is relatively stable over time; the coefficient generally does not show a systematic rise over time.

### Conceptual framework and equations
- Long-run concepts:
  - Potential output: Yt*
  - Natural rate of unemployment: Ut*
- Underlying relationships:
  - (1) Et – Et* = γ (Yt – Yt*) + ηt, γ > 0
  - (2) Ut – Ut* = δ (Et – Et*) + μt, δ < 0
  - Derived Okun’s Law:
    - (3) Ut – Ut* = β (Yt – Yt*) + εt, β < 0, where β = γδ and εt = μt + δηt
- Changes specification:
  - (4) ΔUt = α + β ΔYt + ωt
- Interpretation:
  - β depends on the employment response to output (γ) and the unemployment response to employment (δ).
  - γ is expected to be less than 1.5 (the inverse of a 2/3 labor elasticity), because firms also adjust hours and effort.
  - δ is expected to be less than one in absolute value because labor-force movements offset employment effects on unemployment.
  - Good fit of Okun’s Law means εt is usually small.

### Estimation approaches and methodological notes
- Two primary approaches:
  - Levels equation (3): requires estimation of Ut* and Yt* (typically via HP filter, with alternative methods explored).
  - Changes equation (4): uses ΔUt and ΔYt and implicitly assumes constant Ut* and constant growth of Yt*.
- Smoothing parameters used for HP filter:
  - Annual: λ = 100 and λ = 1,000
  - Quarterly: λ = 1,600 and λ = 16,000
- Quarterly specifications often include two lags of output gap to capture adjustment delays.
- For robustness, alternative measures of Ut* and Yt* considered (e.g., fixing end-of-sample Ut* and growth of Yt* at 2007 values; using forecast errors; using CBO estimates).

### Okun’s Law in the United States — empirical results
- Broad results (annual and quarterly):
  - U.S. Okun’s Law coefficient typically around –0.4 or –0.5, with an R-squared in the neighborhood of 0.8.
- Annual data (1948–2011):
  - Three baseline specifications yield similar results; β ≈ –0.4 and R2 ≈ 0.8.
  - Levels equation with HP parameter λ = 100: coefficient = –0.41 and R2 = 0.82.
  - No evidence of nonlinearities: example (λ = 100) positive output gaps coefficient = –0.37 and negative gaps coefficient = –0.39; p-value for equality = 0.61.
  - Tests for time variation:
    - sup-Wald maximal F statistics = 5.30, 3.99, and 4.49 for the three baseline specs (λ = 100, λ = 1,000, and changes), below the 10 percent critical value of 7.12 (Andrews 2003).
    - Sample-halves coefficients (1948-1979 vs 1980-2011) for levels (λ = 100): –0.35 and –0.41; p-value for equality = 0.20.
    - Decade-by-decade equality cannot be rejected (p-value = 0.38).
- Endpoint/HP-filter issues and alternative end-of-sample assumptions:
  - With HP λ = 100, estimated Ut* rises from about 5 percent in the early 2000s to 8.7 percent in 2011.
  - Growth rate of Yt* over 2008-2011 (HP λ = 100) is 1.3 percent.
  - Alternative construction fixing Ut* and growth of Yt* at 2007 values:
    - Estimated Ut* in 2007 = 4.9 percent
    - Growth rate of Yt* (change 2006–2007) = 2.8 percent
  - Using the alternative end-of-sample Ut* and Yt* produces a regression coefficient of –0.40 (close to baseline –0.41); 2008–2011 observations remain near the regression line.
- Forecast-error approach (Survey of Professional Forecasters, Q1 forecasts 1971–2011):
  - Regression of four-quarter forecast error in unemployment on four-quarter forecast error in output:
    - Coefficient = –0.32 (standard error = 0.03)
    - R2 = 0.68
  - For same sample, regression of actual four-quarter change in Ut on actual change in Yt:
    - Coefficient = –0.37 (standard error = 0.04)
- CBO-based estimates (1980–2011, using CBO Ut* and Yt*):
  - Estimated Okun coefficient = –0.55
  - R2 = 0.89
  - Caution: CBO estimates embed a version of Okun’s Law in the macro model, so these series are not independent evidence.

### Quarterly estimation results
- Levels specification (no lags):
  - Coefficients = –0.43 and –0.41 (for λ = 1,600 and λ = 16,000 respectively)
- Levels specification (with two lags):
  - Current-term coefficients smaller; two lags significant
  - Sums of current and lagged coefficients = –0.49 and –0.45
  - R2 = 0.87 for λ = 1,600 with lags
- Changes specification (quarterly):
  - No lags: coefficient on ΔY = –0.29; R2 = 0.49
  - With lags: sum of coefficients = –0.43; R2 = 0.66
  - Quarterly changes specification is somewhat noisier than levels or annual changes.

### International evidence and special episodes
- Okun’s Law fits most advanced economies; typical R2 is somewhat lower than for the United States.
- The Okun coefficient varies across countries but is relatively stable within countries.
- No general correlation is found between Okun coefficients and the OECD’s measure of legal employment protection.
- Great Recession (2008–2009):
  - Contrary to some international studies suggesting a breakdown, Okun’s Law holds up well once cross-country differences in coefficients and recession lengths are properly accounted for.
  - Apparent anomalies largely disappear under proper accounting.

### Attempts to explain cross-country coefficient differences
- Section VII conducts exploratory analysis with limited success.
- Proposed explanations given for largest outliers (e.g., Spain and Japan), but no variable was found that explains coefficients more generally.
- The Okun coefficient is influenced by costs of adjusting employment (technological/training costs and employment protection laws) and by the marginally attached labor force, but empirical cross-country predictors remain elusive.

### Overall assessment
- Okun’s original specification fits U.S. and most international data across multiple estimation approaches, sample periods, and frequency choices.
- Deviations from Okun’s Law are generally modest and often explained by measurement choices (e.g., HP filter endpoints), differences in national Okun coefficients, or differences in recession timing and length.

*Source: _wp1310 - 1980. Our principal conclusion is that Okun’s Law is a strong and stable relationship in most*

### 2011. Yet our coefficient estimates differ somewhat from those in Okun’s original paper. The

### _wp1310 - 2011. Yet our coefficient estimates differ somewhat from those in Okun’s original paper. The

### Differences in Okun coefficient estimates and sources of variation
- Okun’s original absolute coefficient estimates are close to 0.3; inverting this coefficient he posited the rule of thumb that a one point change in the unemployment rate occurs when output changes by three percent.
- The authors’ coefficient estimates are around –0.4 or –0.5, which fit roughly with modern textbooks that report an inverted coefficient of two.
- The authors investigate why their estimates differ from Okun’s:
  - The natural guess is differences in data (sample period or vintage), but the authors find the key reason is differences in the specification of Okun’s Law.
  - For the changes version of the Law, the key specification issue is lag structure.
  - Okun estimated the changes equation (the authors’ equation (4)) in quarterly data with no lags and, based on 1947Q2 through 1960Q4, reported a coefficient of –0.30.
  - When the authors estimate the same specification for their longer sample, the coefficient is almost the same: -0.29.
  - Larger coefficients in the changes equation arise only if annual data are used or lags are included in the quarterly specification.
- Evidence from Table 3 (quarterly estimates with and without lags of output growth):
  - For Okun’s sample with no lags the estimated coefficient is –0.31 (column 1).
  - For the authors’ full sample with no lags the estimated coefficient is –0.29 (column 3).
  - When two lags are included, the sums of coefficients are –0.44 for Okun’s sample and –0.43 for the full sample (columns 2 and 4).
  - Conclusion: lag structure rather than data differences explains the variation in results.
- Since lags are significant when included, the authors interpret their absence from Okun’s quarterly equation as a modest mis-specification: Okun underestimated the effects of output on unemployment by assuming effects are fully contemporaneous at the quarterly frequency.
- Comparing levels estimates is harder because of differences in series for U* and Y*:
  - Okun assumed U* is 4.0 percent even though unemployment averaged 4.6 over his sample, and he constructed a Y* series that usually exceeds actual output.
  - The authors impose the modern assumption that unemployment and output equal their long run levels on average.
  - These measurement assumptions, along with lag structure, help explain differences in levels results.

### Output, employment, and unemployment (system estimates and implications)
- Data and method:
  - Annual data for 1948-2011.
  - Long-run levels of variables estimated with the HP filter and λ = 100.
  - Equations (1), (2), and (3) estimated jointly as a system of seemingly unrelated regressions (SUR).
- Key parameter estimates (Table 4):
  - The estimate of γ in equation (1), effect of output on employment, is 0.54.
    - Confirms prediction that γ is less than 1.5 but greater in absolute value than the coefficient in Okun’s Law.
  - The estimate of δ in equation (2), effect of employment on unemployment, is –0.73.
    - Confirms prediction that |δ| is less than one.
  - R^2 values: 0.61 for equation (1) and 0.80 for equation (2).
  - SUR estimate of β in Okun’s Law is –0.41, the same as the OLS estimate for the same measures of Y* and U* (see Table 1).
  - Test of non-linear restriction β = γδ (from derivation of Okun’s Law): fail to reject (p-value = 0.38 based on the delta method).
- Interpretation:
  - Scatterplots (Figure 6) confirm these equations fit well, with no major outliers.
  - The joint evidence supports the theoretical derivation linking output → employment → unemployment and the resulting Okun relationship.

### Jobless recoveries and the Great Recession (evidence and interpretation)
- Many observers suggest Okun’s Law has “broken down” with recoveries becoming “jobless” (weaker employment growth and higher unemployment than Okun’s Law predicts).
  - The recoveries from the U.S. recessions of 1990-91, 2001, and 2008-2009 have been called jobless.
- The authors find no evidence of a breakdown in Okun’s Law:
  - Figure 5 shows U.S. unemployment paths consistently fit Okun’s Law predictions, including recent recovery periods.
  - The puzzle: why do many observers perceive a change?
- Analysis of the Great Recession recovery (Figure 7):
  - Paths of output, unemployment, and employment-population ratio from 2007 through 2011 are presented along with long-run level estimates based on pre-recession behavior.
  - Trends estimated with the HP filter through 2007; assume Ut*, growth of Yt*, and growth of long-run employment-population ratio remain at their 2007 levels over 2008-2013.
  - Many describe the period as jobless because the employment-population ratio remained low while output growth returned to normal and level of output surpassed its pre-recession peak in 2011.
- Authors’ quantitative summary (2009–2011 period):
  - The output gap as measured in Figure 7 averaged –10.8 percent.
  - The unemployment gap averaged 4.4 percentage points.
  - The ratio of the two gaps is –0.41, close to earlier estimates of the Okun coefficient.
- Explanation for perceptions of jobless recoveries:
  - Since Okun’s Law relates deviations of unemployment and output from long-run levels, persistent large negative output gaps predict persistent unemployment deviations.
  - Gali et al. (2012): since the 1990s, the speed of recoveries (measured with output growth in the three years after a trough) has been slower than before.
    - Slow growth after troughs in the early 1990s, early 2000s, and after the Great Recession meant sizable output gaps persisted well into recovery, making recoveries appear jobless.
    - In earlier recessions, post-trough above-normal growth pulled output back to trend and employment/unemployment returned to normal, producing job-full recoveries.
  - The authors explain employment behavior in recent recoveries conditional on slow output growth; slow growth may reflect factors such as the zero bound constraining monetary policy since 2008.

### Okun’s Law in 20 advanced economies: fit and comparative results
- Sample and data:
  - 20 countries: populations above one million that were OECD members in 1985.
  - Annual data on output and unemployment from the OECD.
  - Period examined: 1980-2011 (start in 1980 because pre-1980 unemployment was extremely low in some countries).
- Basic results (Table 5, λ = 100 for U* and Y*):
  - The fit is good for most countries, though usually not as close as for the United States.
  - R^2 exceeds 0.4 in all countries but Austria and Italy.
  - Spain: R^2 of 0.90 (highest).
  - Estimated coefficients on the output gap vary across countries:
    - Most spread between –0.23 and –0.54.
    - Two countries lower in absolute value: Austria and Japan.
    - Spain is an outlier with –0.85.
  - Japan: R^2 = 0.74 and coefficient –0.16 (small unemployment movements well explained by output movements and a low coefficient).
- Robustness and averages:
  - Results also estimated with HP parameter λ = 1,000 for U* and Y*, and Okun’s Law in changes; qualitatively similar though fit not as close for some countries.
  - Averaging across the 20 countries:
    - The R^2 is 0.63 for λ = 100 results in Table 5.
    - The R^2 is 0.59 for λ = 1,000.
    - The R^2 is 0.49 for the changes equation.
    - The average coefficients for the three specifications are –0.40, –0.37, and –0.33.
- Note:
  - Results are presented for OECD national definitions of unemployment; similar results obtain using the OECD’s harmonized unemployment series.
  - Coefficients estimated with OLS for each country; similar results if estimated jointly in a panel framework with SUR.

### Stability of Okun’s coefficient over time across countries
- Question: Is the Okun coefficient stable over time within countries?
  - Previous literature: Cazes et al. (2012) find erratic variation; IMF (2010) finds the coefficient generally rose over time (attributed to legal reforms reducing firing costs).
- Authors’ simple stability check:
  - Estimate separate coefficients for 1980-1995 and 1996-2011 for each country (results in Table 6).
- Findings:
  - Some evidence of instability: for seven of the 20 countries, equality of first-half and second-half coefficients can be rejected at the five percent level.
  - However, in five out of these seven cases the coefficient is lower in absolute value in the second half of the sample.
  - The average coefficient across the 20 countries:
    - –0.43 in the first half of the sample.
    - –0.36 in the second half of the sample.
  - The authors’ data generally do not support the view that the Okun coefficient has risen over time.
  - Differences across countries are similar in the two periods (e.g., Spain highest in both periods; Austria and Japan lowest).
  - Correlation of coefficients across the two periods is 0.49.

### Okun’s Law in the Great Recession
- Skepticism about Okun’s Law increased after the Great Recession of 2008- (text cuts off here in the supplied excerpt).

*Italic: Source content from the supplied IMF PDF excerpt.*

### 2009.  One  reason,  emphasized  by  IMF  (2010)  and  McKinsey  (2011),  is  that  there  is  little

### _wp1310 - 2009.  One  reason,  emphasized  by  IMF  (2010)  and  McKinsey  (2011),  is  that  there  is  little

### A. Output and Unemployment from Peak to Trough
- Nineteen of the countries in the sample (all but Australia) experienced a recession beginning in either late 2007 or 2008, according to Harding and Pagan’s (2002) definitions of peaks and troughs in output.
- Figure 9a plots the change in output from peak to trough against the change in unemployment over the same period; changes in output and unemployment are uncorrelated across countries.
- When the change in U is regressed on a constant and the change in Y, the R^2 is –0.03.
- Examples cited as evidence against Okun’s Law: Germany and the United Kingdom had larger output falls than the United States and Spain, yet unemployment increased by less in the U.K. and fell in Germany.
- Proposed novel explanations for cross-country unemployment changes include:
  - IMF (2010): financial crises and house price busts raise unemployment for a given level of output.
  - McKinsey (2011): output growth may fail to decrease unemployment because workers lack the skills for available jobs.

### B. Correcting for the Length of Recessions
- Recession lengths vary across countries; for the recessions in Figure 9a the period from peak to trough ranges from two quarters in Portugal to seven quarters in Demark.
- Okun’s Law in changes (quarterly) is specified as ΔU_t = α + β ΔY_t, with α > 0, β < 0.
- Cumulating over T quarters gives Σ ΔU = α T + β Σ ΔY.
- Intuition: α > 0 because potential output grows over time; holding constant the change in output, a longer recession implies a larger rise in unemployment.
- Regression of cumulative change in U on cumulative change in Y and recession length T (without a constant) yields:
  - α = 0.70 (standard error = 0.30)
  - β = –0.12 (standard error = 0.25)
- This regression explains a substantial part of cross-country variation in Σ ΔU: R^2 is 0.54.
- Spain’s large increase in unemployment is partly explained by the length of its recession—six quarters, the second-longest in the sample.

### C. Adjusting for Country-Specific Coefficients
- Allowing country-specific Okun parameters: Σ ΔU = α_i T + β_i Σ ΔY, where α_i and β_i are country i’s parameters.
- For α_i and β_i, authors use estimates of Okun’s Law in changes for annual data over 1980-2011 (with α_i divided by four to fit quarterly data).
- The α_i’s average 0.87 across countries (0.22 once we divide by four).
- The β_i’s are highly correlated with Okun coefficients in Table 5 (estimated with the levels version of Okun’s Law).
- Comparing actual and fitted Σ ΔU from equation (8) yields R^2 = 0.76.
- Spain’s large rise in unemployment is explained almost entirely by its unusually large Okun coefficient β_i combined with the length of its recession.

### D. A German Miracle?
- Germany is the one country in the sample where unemployment fell during its recession; this outcome is often called a “miracle.”
- Work-sharing (decreases in hours per worker) encouraged by government subsidies to employers who retained workers is a common explanation.
- Figure 9c shows Germany deviated from Okun’s Law during its recession:
  - Predicted change in unemployment for Germany: 2.2 percentage points.
  - Actual change in unemployment for Germany: –0.3 percentage points.
- The residual for Germany is modest compared to cross-country differences in unemployment changes; “miracle” may be an exaggeration.

### VII. Explaining Cross-Country Variation in Okun’s Law
- Most countries have a well-fitting Okun relationship, but the Okun coefficient differs substantially across countries.

A. Looking for Explanatory Variables
- Figure 10 plots estimated Okun coefficients for 20 countries against average unemployment over 1980-2011 (left panel): an inverse relationship is observed—higher average unemployment associated with larger fluctuations in response to output movements.
- The result is driven by a cluster of countries with low unemployment and low coefficients (Switzerland, Japan, Austria, Norway) and by Spain with very high unemployment and a very high coefficient.
- Tests of the OECD’s overall EPL index (averaged over 1985-2008) against the Okun coefficient (right panel) find:
  - The relationship has the wrong sign and is statistically insignificant.
  - Footnote: For New Zealand, the EPL index is available over 1990-2008. No relationship is found between the Okun coefficient and components of the EPL index.

B. Individual Countries
- Idiosyncratic labor-market features likely account for most variation in the Okun coefficient; single measurable variables do not explain it fully.

Spain
- Okun coefficient: –0.85 (much higher in absolute value than any other country’s).
- Likely explanation: unusually high incidence of temporary employment contracts; such contracts have accounted for around a third of Spanish employment over the 1990s and 2000s.
- Temporary contracts make it easier for firms to adjust employment when output changes, raising the Okun coefficient.
- OECD’s EPL index assigns a fairly high number to Spain, but observers argue the index does not capture non-enforcement of de jure restrictions on fixed-term contracts.

Japan
- Okun coefficient: –0.16 (second smallest in absolute value).
- Likely explanation: tradition of “lifetime employment,” making firms reluctant to lay off workers; this employer choice is not captured by the EPL index.
- Ono (2010) reports the lifetime-employment tradition has weakened; Japan is one of two countries with a statistically significant increase in the coefficient from the first half to the second half of the sample, though the coefficient remains under 0.2 in both parts.

Switzerland
- Okun coefficient: –0.24 (third smallest).
- Likely explanation: large use of foreign workers; when employment changes, migrant workers move in and out, so changes in employment are accommodated by changes in the labor force and unemployment is stable.
- Decomposing Okun into its components:
  - Switzerland’s coefficient in the E-Y equation: 0.46 (near the middle of the range for the 20 countries).
  - Switzerland’s coefficient in the U-E equation: –0.17 (the second smallest, statistically insignificant).
- Conclusion: Switzerland’s unusual feature is the non-responsiveness of unemployment to employment.

Austria
- Okun coefficient: –0.14 (the smallest for the 20 countries).
- Both the E-Y and U-E estimated coefficients are implausibly small—less than 0.02 in absolute value.
- No explanation is provided; further investigation left to future research.

### VIII. Conclusion
- Okun’s Law is a robust macroeconomic relationship: strong and stable by the standards of macroeconomics, though not universal (parameters differ across advanced economies).
- Reports of deviations from the Law are often exaggerated; Okun’s Law is more reliable than many macro relationships such as the Phillips curve.
- Evidence is consistent with traditional macro models where shifts in aggregate demand cause short-run fluctuations in unemployment; the evidence does not rule out other theories (sectoral shocks, extensions of unemployment benefits).
- A puzzle remains: the Okun coefficient is far smaller than would be expected from an inverted production function (even using employment rather than unemployment on the left side). Traditional macro explains this via costs of adjusting employment to aggregate demand shifts; it is unclear whether a small Okun coefficient arises naturally in alternative unemployment models.
- The usefulness of Okun’s Law in testing macro theories is a topic for future research.

*Source: Excerpt from the provided IMF working paper content.*

### 1. United States: Estimates of Okun’s Law

### 1. United States: Estimates of Okun’s Law

### Annual estimates (1948-2011)
- Equation in levels: U_t – U_t* = β (Y_t – Y_t*) + ε_t
  - Hodrick-Prescott filter λ = 100: β = -0.411*** (0.024); Obs 64; Adjusted R^2 0.817; RMSE 0.426
  - Hodrick-Prescott filter λ = 1,000: β = -0.383*** (0.023); Obs 64; Adjusted R^2 0.813; RMSE 0.524
- Equation in first differences: ΔU_t = α + β ΔY_t + ε_t
  - β = -0.405*** (0.029); α = 1.349*** (0.116); Obs 63; Adjusted R^2 0.752; RMSE 0.556
- Significance notation: ***, **, and * indicate statistical significance at the 1, 5, and 10 percent level.

### Quarterly estimates (1948Q2-2011Q4)
- Equation in levels with lag polynomial β(L) and various specifications (reported point estimates and standard errors in parentheses):
  - β0 = -0.428*** ( 0.015); β1 = -0.133*** ( 0.0345); β2 = -0.116*** ( 0.0230)
    - β0 + β1 + β2 = -0.494*** ( 0.0126)
    - α = 0.359*** ( 0.0215)
    - Obs 256; Adjusted R^2 0.767; RMSE 0.398
  - Alternative specification: β0 = -0.245*** ( 0.0230); β1 = -0.153*** ( 0.0447); β2 = -0.0794*** ( 0.0286)
    - β0 + β1 + β2 = -0.445*** ( 0.0119)
    - Obs 256; Adjusted R^2 0.865; RMSE 0.302
  - Alternative specification: β0 = -0.411*** ( 0.013); β1 = -0.137*** ( 0.0168); β2 = -0.0767*** ( 0.0160)
    - β0 + β1 + β2 = -0.432*** ( 0.0200)
    - Obs 256; Adjusted R^2 0.795; RMSE 0.463
  - Two additional reported columns (smaller sample sizes): β0 = -0.213*** ( 0.0286) and β0 = -0.286*** ( 0.018) with respective RMSEs 0.394 and 0.287 and Adjusted R^2 0.852 and 0.494; other Obs reported as 256, 255, 255.
- Equation in first differences (quarterly): ΔU_t = α + β(L) ΔY_t + ε_t — see quarterly columns above for Δ-specification counterparts.

### Replication and update of Okun (1962) (Quarterly data)
- Equation: ΔU_t = α + β(L) ΔY_t + ε_t
  - Column (1) (sample 1948Q2-1960Q4, vintage data): β0 = -0.307*** (0.036); β1 = -0.168*** ( 0.0327); β2 = -0.0394 ( 0.0307); β0 + β1 + β2 = -0.441*** ( 0.0380); α = 0.305*** (0.061); Obs 51; Adjusted R^2 0.584; RMSE 0.382
  - Column (2) (sample 1948Q2-2011Q4, vintage data): β0 = -0.233*** ( 0.0303); β1 = -0.137*** ( 0.0168); β0 + β1 + β2 = -0.432*** ( 0.0200); α = 0.424*** ( 0.0524); Obs 125; Adjusted R^2 0.758; RMSE 0.292
  - Column (3) and (4) (current data): Column (3): β0 = -0.286*** (0.018); α = 0.244*** (0.023); Obs 52; Adjusted R^2 0.494; RMSE 0.287. Column (4): β0 = -0.218*** (0.0160); α = 0.359*** (0.0215); Obs 255; Adjusted R^2 0.663; RMSE 0.234.

### Okun’s Law and Unemployment–Employment relation (Annual, 1948-2011; SUR estimates)
- Jointly estimated equations (E denotes log of employment; natural rates based on HPF with λ = 100):
  1) E_t – E_t* = γ (Y_t – Y_t*) + η_t  (Okun’s Law for Employment)
     - γ = 0.543*** (0.040); Obs 64; Adjusted R^2 0.610
  2) U_t – U_t* = δ (E_t – E_t*) + μ_t  (Unemployment–Employment Relation)
     - δ = -0.728*** (0.027); Obs 64; Adjusted R^2 0.798
  3) U_t – U_t* = β (Y_t – Y_t*) + ε_t  (Okun’s Law for Unemployment)
     - β = -0.405*** (0.024); Obs 64; Adjusted R^2 0.820
- Reported p-value for H0: β = γδ is 0.378.

### Cross-country estimates: 20 advanced economies (Annual, 1980-2011)
- Equation: U_t – U_t* = β (Y_t – Y_t*) + ε_t (natural rates based on HPF with λ = 100)
- Selected country β estimates (point estimate, standard error, Obs, Adjusted R^2, RMSE):
  - Australia: β = -0.536*** ( 0.0476); Obs 32; Adjusted R^2 0.797; RMSE 0.439
  - Austria: β = -0.136*** ( 0.0438); Obs 32; Adjusted R^2 0.213; RMSE 0.375
  - Belgium: β = -0.511*** ( 0.0817); Obs 32; Adjusted R^2 0.543; RMSE 0.708
  - Canada: β = -0.432*** ( 0.0374); Obs 32; Adjusted R^2 0.805; RMSE 0.495
  - Denmark: β = -0.434*** ( 0.0471); Obs 32; Adjusted R^2 0.724; RMSE 0.570
  - Finland: β = -0.504*** ( 0.0485); Obs 32; Adjusted R^2 0.770; RMSE 1.025
  - France: β = -0.367*** ( 0.0441); Obs 32; Adjusted R^2 0.681; RMSE 0.394
  - Germany: β = -0.367*** ( 0.0629); Obs 32; Adjusted R^2 0.508; RMSE 0.689
  - Ireland: β = -0.406*** ( 0.0395); Obs 32; Adjusted R^2 0.766; RMSE 0.835
  - Italy: β = -0.254*** ( 0.0672); Obs 32; Adjusted R^2 0.292; RMSE 0.654
  - Japan: β = -0.152*** ( 0.0194); Obs 32; Adjusted R^2 0.654; RMSE 0.229
  - Netherlands: β = -0.511*** ( 0.0705); Obs 32; Adjusted R^2 0.617; RMSE 0.722
  - New Zealand: β = -0.341*** ( 0.0493); Obs 32; Adjusted R^2 0.594; RMSE 0.705
  - Norway: β = -0.294*** ( 0.0406); Obs 32; Adjusted R^2 0.617; RMSE 0.449
  - Portugal: β = -0.268*** ( 0.0371); Obs 32; Adjusted R^2 0.615; RMSE 0.629
  - Spain: β = -0.852*** ( 0.0503); Obs 32; Adjusted R^2 0.899; RMSE 0.757
  - Sweden: β = -0.524*** ( 0.0719); Obs 32; Adjusted R^2 0.619; RMSE 1.002
  - Switzerland: β = -0.234*** ( 0.0458); Obs 32; Adjusted R^2 0.439; RMSE 0.434
  - United Kingdom: β = -0.343*** ( 0.0495); Obs 32; Adjusted R^2 0.595; RMSE 0.699
  - United States: β = -0.454*** ( 0.0373); Obs 32; Adjusted R^2 0.821; RMSE 0.418

### Pre-1995 vs post-1995 split (1980-1994 and 1995-2011)
- Estimation: U_t – U_t* = β_pre-95 (Y_t – Y_t*) + β_post-95 (Y_t – Y_t*) + ε_t
- Selected country coefficient splits and p-values for equality test:
  - Australia: β_pre-95 = -0.552*** ( 0.051); β_post-95 = -0.433*** ( 0.131); p-value 0.405; Obs 32; Adjusted R^2 0.796; RMSE 0.441
  - Canada: β_pre-95 = -0.500*** ( 0.041); β_post-95 = -0.287*** ( 0.059); p-value 0.006; Obs 32; Adjusted R^2 0.844; RMSE 0.442
  - Finland: β_pre-95 = -0.610*** ( 0.051); β_post-95 = -0.297*** ( 0.071); p-value 0.001; Obs 32; Adjusted R^2 0.833; RMSE 0.872
  - Japan: β_pre-95 = -0.109*** ( 0.023); β_post-95 = -0.209*** ( 0.027); p-value 0.008; Obs 32; Adjusted R^2 0.718; RMSE 0.206
  - Netherlands: β_pre-95 = -0.713*** ( 0.092); β_post-95 = -0.336*** ( 0.086); p-value 0.006; Obs 32; Adjusted R^2 0.695; RMSE 0.645
  - Portugal: β_pre-95 = -0.221*** ( 0.037); β_post-95 = -0.463*** ( 0.0755); p-value 0.007; Obs 32; Adjusted R^2 0.688; RMSE 0.567
  - Sweden: β_pre-95 = -0.648*** ( 0.091); β_post-95 = -0.362*** ( 0.104); p-value 0.046; Obs 32; Adjusted R^2 0.656; RMSE 0.953
  - United Kingdom: β_pre-95 = -0.419*** ( 0.059); β_post-95 = -0.215*** ( 0.077); p-value 0.045; Obs 32; Adjusted R^2 0.635; RMSE 0.663
  - United States: β_pre-95 = -0.447*** ( 0.050); β_post-95 = -0.464*** ( 0.058); p-value 0.829; Obs 32; Adjusted R^2 0.815; RMSE 0.425
- Notes: β_pre-95 denotes 1980-1994 sample; β_post-95 denotes 1995-2011 sample.

### Tests for coefficient stability and robustness
- Figure 2: Reports F statistic for break in Okun coefficient (β) for each date in the conventional inner 70 percent of the sample; critical value from Andrews (2003). Plots shown for λ = 100, λ = 1,000, and first differences.
- Figure 3 (Robustness: U.S. natural rates):
  - Panel a: Unemployment rate actual and natural (HPF λ = 100).
  - Panel b: Output actual and natural.
  - Panel c: HPF based on data through 2007, no-change assumption for 2008-11.
- Figure 4: Okun’s Law based on forecast errors (forecast errors for four-quarter-ahead forecasts of four-quarter changes, 1971Q1-2011Q1) using Survey of Professional Forecasters.
- Figure 5: Actual and fitted unemployment rate from quarterly Okun specification in levels with two lags and natural rates HPF λ = 100.
- Figures 6–9: Visual diagnostics relating Okun’s Law for employment, unemployment–employment relation, and comparisons for the Great Recession and 1981 recession; cumulative peak-to-trough Σ ΔU and Σ ΔY comparisons with adjustments for recession duration T and country-specific Okun coefficients α_i and β_i.
- Figure 10: Cross-country scatterplots of Okun coefficient versus candidate variables (e.g., average unemployment rate 1980-2011 mean; OECD overall employment protection index 1985-2011 mean).

*Source: _wp1310 - 1. United States: Estimates of Okun’s Law (annual and quarterly estimates, robustness checks, SUR estimation for employment relation, cross-country comparisons) based on Hodrick-Prescott filter specifications and vintage/current data as reported in the source content.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp1310.pdf_