## wp18138 ## Source details **Canonical URL:** [wp18138](https://www.imf.org/-/media/files/publications/wp/2018/wp18138.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2018/wp18138.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2018/wp18138.pdf.json) --- ### Introduction and motivation - Job growth in the U.S. has been robust since the end of the great recession and has converged to rates seen at end-2006. - Unemployment has fallen steadily and is now near levels not seen since the late 1960s. - Wage growth has remained subdued: - U.S. hourly earnings have grown by 3.2 percent year-on-year, on average, in the new millennium through end-2007 (pre-GR). This is 1.5 times the average growth to date since the end of the recession. - The Employment Cost Index (ECI) for worker compensation indicates a pre-to-post GR wage growth ratio of almost 2. ### Research questions and empirical approach - Key questions: - Has the relationship between labor market slack and wage growth weakened after the global financial crisis? - Is the economy close to full employment, or does subdued wage growth signal more slack than the headline unemployment rate implies? - Does slower labor productivity growth depress wage growth, and by how much? - Can the model’s estimated coefficients and the time path of wage growth determinants track recent wage dynamics? - Methodology: - Macro: General-to-specific Phillips-curve framework; cointegration analysis using Johansen’s maximum-likelihood VAR procedure; annualized log differences of quarterly level data; VAR sample 1990Q1-2017Q3. - Micro: Augmented Mincer-type model using Current Population Survey (CPS) March samples 1997–2017; controls for education, gender, employment characteristics, occupation/industry exposure, and local labor market slack. ### Main contributions and high-level findings - Macro (wage Phillips curve) results: - Weak wage growth is mostly a product of low labor productivity growth. - Model fits the data well; parameters show no sign of structural instability; the null hypothesis of linearity cannot be rejected. - Decomposition: upward pressure from diminishing labor market slack during the recovery offset by contemporaneous decline in labor productivity growth. - Additional downward pressures on real compensation growth: technological progress (automation of routine tasks), falling unionization rates, and trade globalization. - Results robust to alternative wage and slack measures. - Micro (individual-level) results: - Lower local/regional unemployment puts upward pressure on wage growth, but this effect has become weaker than in the pre-2008 period — implying a flattening of the wage-unemployment relationship after accounting for structural changes. - Downward pressure on wages for individuals in occupations exposed to automation and offshoring. - Downward pressure on wages in industries with higher concentration of large firms (consistent with monopsony power concerns). - College-educated workers in routinizable jobs and in more concentrated industries face additional downward pressure; less-educated workers face a wage discount when employed in offshorable tasks. - Multiple correlated factors (technology, globalization, market concentration) jointly contribute to weak wage growth. ### Macro analysis — cointegration and the long run - Variables and treatment: - VAR variables: ∆w_t (ECI for compensation in nonfarm business), ∆p_t (PCE price index), ∆y_t (real output per hour in nonfarm business). - Growth rates treated as I(1); VAR sample 1990Q1-2017Q3. - Johansen evidence: - Strongly rejects the null of no cointegration in favor of at least one cointegrating relationship. - Cannot reject the null of at most one relationship in favor of more than one — evidence points to a unique cointegrating vector. - Estimated cointegrating coefficients on ∆p_t and ∆y_t have the right signs, are statistically significant, and are numerically close to minus unity. - Likelihood ratio tests do not reject coefficients equal to minus one, individually or jointly. - Final restricted long-run representation: - ∆푤ₜ = −0.9 + ∆푝ₜ + ∆푦ₜ - Interpretation: - Long-run wage inflation increases with price inflation and labor productivity growth. - The constant −0.9 captures the secular decline in the labor share of income over 1990-2017 and reflects that wages have fallen short of the sum of productivity and inflation growth over the period. - Industry- and state-level analysis attributes most of the labor-share fall to technological changes linked to automation of routine tasks, followed by trade globalization; declines in unionization also contributed. ### Additional cointegration diagnostics and stationarity tests - Multivariate stationarity tests (Johansen 1995) strongly reject stationarity of ECI growth, inflation, and productivity growth (p-values effectively zero). - Tests preclude a stationary linear combination of the variables in levels; graphical series (w_t − p_t − y_t) displays a downward trending, apparently nonstationary series. - The series ∆w_t +0.9 − ∆p_t − ∆y_t exhibits mean reversion (Figure 3). - Augmenting the VAR with the CBO unemployment gap still yields one cointegrating vector; coefficient on the unemployment gap in the cointegrating vector is very small and statistically indistinguishable from zero: Chi^2(1) = 0.77 [0.381]. ### Role of labor market slack (long run vs short run) - Conceptual point: labor market slack should not affect wage growth in the long run. - Empirical finding: slack (CBO unemployment gap) does not affect the long-run cointegrating relationship but matters in the short run. ### Short run — estimation strategy and ADL specification - Two-step approach: 1. Trend wage growth from cointegrating relationship using: - ∆p_t^trend = expected long run (10 yr.) PCE inflation from SPF. - ∆y_t^trend constructed via Baxter and King (1999) band-pass filter with Staiger, Stock, and Watson (2001) settings. 2. Wage growth gap (actual minus trend) modeled as an ADL on the unemployment gap. - Final ADL specification (equations 2 and 3): - ∆w_t − ∆p_t^trend − ∆y_t^trend = θ + ∑_{s=0}^{4} λ_s (U_{t−s} − U*_{t−s}) + ε_t - Equivalently: ∆w_t = θ + ∆p_t^trend + ∆y_t^trend + ∑_{s=0}^{4} λ_s Ugap_{t−s} + ε_t - Empirical simplifications supported: - Lags on the wage growth gap were not statistically significant. - Lags on the unemployment gap beyond the first did not matter; final model uses contemporaneous and short lags up to 4 quarters. ### General unrestricted wage Phillips curve and model reduction - General specification (equation 4) nests inertia, forward-looking behavior, indexation, trend productivity, and potential error-correction term. - Model reduction tests (sample 1990Q1-2017Q3) support simplifying to parsimonious specification EQ(g) corresponding to equation 3: - Key test outcomes: - EQ(a) → EQ(b): F(12,82) = 0.650 [0.7934] - EQ(b) → EQ(c): F(4,94) = 0.979 [0.4228] - EQ(a) → EQ(c): F(16,82) = 0.721 [0.7649] - Specific validated restrictions: - Lags 5–8 coefficients jointly zero (realized F = 0.65 p-value = 0.793). - Lags beyond first on unemployment gap not significant. - Error correction term α estimated as zero (consistent with multivariate non-stationarity). ### Baseline model properties and key quantitative messages - Baseline model corresponds to equation 3; estimation sample 1990Q1-2017Q3. - Main features: - Negative and highly statistically significant constant term of about one percent (headwinds to wage growth). - The slope of the wage Phillips curve equals the sum of coefficients on current and lagged unemployment gap; it is negative and highly statistically significant. - Estimated short-run labor market sensitivity: - A one percentage point reduction in the unemployment gap implies, on average, a 0.311 percentage point increase in wage growth (cumulative impact ≈ -0.311). - Selected reported statistics and diagnostics: - R-squared : 0.496 - S.E. of regression: 0.778 (reported) and 0.786 (other block) - Representative parameter rows reported: - -1.127 0.633 -1.78 0.0780 and -1.100 0.086 -12.80 0.000 - -0.311 0.051 -6.13 0.0000 and -0.311 0.050 -6.27 0.0000 - 1.017 0.152 6.69 0.0000 - 0.993 0.192 5.18 0.0000 - Testing restrictions: Chi^2(2) = 0.020637 [0.9897] ### Model performance, parameter stability, and diagnostics - Baseline model: “statistically well-behaved,” with reasonably good fit and pseudo out-of-sample forecasts tracking realized data. - Residual diagnostics: residuals look stationary; formal tests do not reject serial uncorrelation, homoscedasticity, and normality; no evidence of an ARCH process. - Recursive estimation: parameters show remarkable stability over time; normalized recursive chow tests do not reject parameter constancy — evidence against the hypothesis that the global financial crisis made the wage Phillips curve flatter. ### Decomposition of ECI growth and interpretation - Decomposition drivers: Inflation Expectations, Trend Productivity, Constant (other headwinds), Slack, Other. - Historical contributions since 2000: - High labor market slack during the great recession and moderating productivity growth weighed on wage growth. - Rising labor utilization during recovery exerted upward pressure on compensation growth, offset by declining contribution from productivity growth and negative contribution from the constant term. - Interpretation: augmenting the wage Phillips curve with labor productivity growth resolves the “missing” wage growth — wages are where they should be given productivity and inflation trends plus a secular labor-share decline. ### Robustness to alternative slack measures and nonlinearities - Alternative slack concepts: U6 and UST (short-term unemployment). - Estimated cumulative impacts (estimation sample 1990Q1-2017Q3): - Baseline (U3-based) cumulative impact: -0.311 (Est.s.e. 0.050, t-value -6.27, t-prob 0.000). - U6 model cumulative impact: -0.181 (Est.s.e. 0.029, t-value -6.14, t-prob 0.000). - UST model cumulative impact (memo): -1.135 (Est.s.e. 0.103, t-value -10.97, t-prob 0.000); table reports a coefficient block showing -0.661 (Est.s.e. 0.114, t-value -5.83, t-prob 0.000). - R-squared: Baseline 0.496; U6 0.469; UST 0.490. - S.E. of regression: Baseline 0.778; U6 0.797; UST 0.783. - Interpretation: as slack is broadened (U3 → U6 → UST), sample variance of the gap increases, covariance with wage growth increases more slowly, so the slope falls; contributions of slack to ECI growth change little across slack concepts. - Nonlinearity tests: - Quadratic unemployment gap coefficient imprecisely estimated; null of linearity cannot be rejected; nonlinear model reduces to baseline. - Kalman filter natural rate: - Natural rate modeled as random walk and jointly estimated with augmented Phillips curve. - Kalman-filter natural rate and CBO series display very similar behavior; maximum difference about 0.3 percentage points over 2009–14. - Recent readings: both series put the natural rate below 4.8 percent. - Phillips curve coefficient estimates using Kalman-filter natural rate very similar to baseline. ### Alternative macro wage measures (robustness) - Alternative wage series: ECI for wages and salaries, average hourly earnings of production and nonsupervisory employees, compensation per hour in nonfarm business, Atlanta Fed wage tracker. - Johansen cointegration tests for alternatives: one and only one cointegrating relationship in all models — nominal wage growth depends on inflation and productivity growth with coefficient of unity on each. - Short-run dynamics with alternative wage measures: - Lagged dependent variable often matters, yielding larger cumulative impacts of slack on wage growth. - Reported cumulative effects range from -0.372 to -0.557 across measures (text summary). - Comparisons: Gordon (1998) estimate -0.43; Staiger, Stock, and Watson (2001) state-level regressions yield -0.526 — comparable to the paper’s alternative-measure estimates (e.g., -0.372 and -0.482 reported). ### Micro analysis — data, structural indices, and specification - Data: CPS March sample 1997–2017; baseline sample observations 164,478. - Structural indices: - Routinization Score: occupation propensity to automate routine tasks (O*NET 2001). - Offshorability Score: occupation potential to be offshored (O*NET 2001). - Employment concentration: share of workers in two-digit industry employed in firms with 500+ employees (time-varying CPS ASEC). - Local labor market slack: state-level unemployment gap ugap_rt = u_rt − û_rt, where û_rt is average U.S. state unemployment rate during 2000-2005. - Baseline micro specification: log hourly wage regressed on controls, local unemployment gap, routinization, offshorability, employment concentration, and interaction terms with education groups; includes state and year fixed effects. ### Principal micro results (selected) - Full-sample (1997-2017) direct effects: - Routinization index: coefficient -0.0021* (s.e. 0.0011) in one column; other specifications show similar small negative effects. - Offshorability index: coefficient -0.0402*** (s.e. 0.0012) — occupation offshorability reduces wages by 4.02 percent holding controls constant. - Employment concentration: coefficient -0.2662*** (s.e. 0.0073) — a rise of the concentration ratio by 0.1 points (10 percentage points more concentrated industry) associated with a wage penalty of 2.7 percent (as interpreted in text). - Interaction results by education (selected): - Routinization primarily affects college-educated workers: college+ penalty of -5.9 percent for a 1 standard deviation higher routinization score (column 4C+ reported as -0.0589***). - Offshorability: lower-skill groups bear larger penalty; combined direct and interaction effects for lower skill ≈ -5.2 percent; skilled workers net out better (+3.2 percent = -5.2 direct + 8.4 interaction). - Employment concentration: being in a sector with 10 percentage points higher share of large employers reduces wages by 3.7 percent for the skilled relative to 1.5 percent for lower-skill workers (columns 4C+ and 4HS reported as -0.3745*** and -0.1525*** respectively). - Micro-effect magnitudes: - Individual structural effects range between about -1 to -7 percent; when combined they can sum to economically meaningful impacts. - Technological change and market power effects appear larger for skilled workers. ### Micro robustness checks and additional results - Robustness dimensions: - Restrict to full-time workers; restrict to males; add industry-level openness/import competition controls; sample of workers with consecutive-year observations to examine wage growth and churning. - Selected robustness table outcomes (Table 8): - Model 1 (All): Routinization -0.0078** (0.0032); Offshorability -0.0522*** (0.0035); Employment concentration -0.0859*** (0.0182); Observations 164,478; R-squared 0.4234. - Model 2 (Full time): Routinization -0.0112**; Offshorability -0.0830***; Employment concentration -0.0571**; Observations 108,501; R-squared 0.3650. - Model 3 (Men): Offshorability -0.0830***; Employment concentration -0.1304***; Observations 80,298; R-squared 0.4366. - Model 4 (Int’l factors added): coefficients broadly unchanged; Observations 144,980; R-squared 0.4232. - Model 5 (annual wage growth, panel): structural variables retain negative signs but with smaller statistical significance; Observations 202,326; R-squared 0.0038. - Conclusion: results largely robust to alternative samples and controls; full-time workers appear more vulnerable to occupation-specific structural changes. ### Micro evidence on labor market slack and apparent flattening - Panel wage specifications with unemployment gap (lag 12 months) and structural controls (Rout, Off, MP) — Table 9 selected estimates: - 1997-2017 (model 1): Unemp gap (lag 12m) = -0.0122*** (0.0011) — after 12 months, a one percent increase in unemployment gap lowers nominal wages by around 1.22 percent. - 1997-2007 (model 2): Unemp gap = -0.0096*** (0.0023). - 2010-2017 (model 3): Unemp gap = -0.0037 (0.0023) — effect has declined post-GFC. - Piecewise and quadratic specifications show little robust evidence of a kink; nonlinear terms often insignificant. - Interpretation: the wage effect of slack has fallen by more than half when comparing pre- and post-GFC periods; controlling for structural variables, the post-GFC flattening of the micro Phillips curve remains — one possible mechanism is a decline in voluntary labor turnover reducing reallocation and competition for jobs. ### Conclusions and overarching takeaways - Macro findings: - Productivity-augmented Phillips curve explains broad wage dynamics well. - Main macro drivers of lackluster wage growth: persistent weakening in trend labor productivity growth and secular decline in the labor share (captured by negative constant term). - Macro results robust to alternative slack and wage measures; recursive tests indicate parameter stability (no structural break at GFC). - Micro findings: - Micro-econometric analysis identifies multiple structural contributors to wage moderation: routinization (automation exposure), offshorability, and employment concentration (industry market power). - Offshorability and employment concentration have larger negative effects on wages in levels; routinization effects concentrated among college-educated workers. - Micro model suggests a significant decline in the absolute value of the wage Phillips curve slope after 2009, implying an additional labor-market related contributor to wage moderation not captured in aggregate stability tests. - Overall assessment: - Technology, globalization, and market power have each contributed to wage moderation; their correlated trends and causal links complicate clean decomposition of relative importance. - Both macro and micro evidence imply that multiple forces together account for the prolonged modest wage growth. *Source: wp18138 (excerpt from IMF working paper PDF).* ### REFERENCES ___________________________________________________________30 ### REFERENCES ### Introduction and motivation - Job growth in the U.S. has been robust since the end of the great recession and has converged to rates seen at end-2006. - Unemployment has fallen steadily and is now near levels not seen since the late 1960s. - Wage growth has remained subdued: - U.S. hourly earnings have grown by 3.2 percent year-on-year, on average, in the new millennium through end-2007 (pre-GR). This is 1.5 times the average growth to date since the end of the recession. - The Employment Cost Index (ECI) for worker compensation indicates a pre-to-post GR wage growth ratio of almost 2. ### Research questions and approach - Key questions examined: - Has the relationship between labor market slack and wage growth weakened after the global financial crisis? - Is the economy close to full employment, or does subdued wage growth signal more slack than the headline unemployment rate implies? - Does slower labor productivity growth depress wage growth, and by how much? - Can the model’s estimated coefficients and the time path of wage growth determinants track recent wage dynamics? - Methodology: - Battery of empirical exercises combining macro-econometric models with aggregate data and micro-econometric wage models using individual-level data. - Macro: General-to-specific Phillips-curve framework nesting competing explanations; rich dynamics; cointegration analysis. - Micro: Augmented Mincer-type model using Current Population Survey data, controlling for education, gender, employment characteristics, and occupation/industry exposure. ### Main contributions and high-level findings - Macro (wage Phillips curve) results: - Weak wage growth is mostly a product of low labor productivity growth. - The model fits the data well; parameters show no sign of structural instability; the null hypothesis of linearity cannot be rejected. - Decomposition shows upward pressure on compensation growth from diminishing labor market slack during the current recovery, offset by a contemporaneous decline in labor productivity growth. - Additional downward pressures on real compensation growth: technological progress (automation of routine tasks), falling unionization rates, and trade globalization. - Results are robust to alternative wage and slack measures. - Micro results (individual-level analysis): - Lower local/regional unemployment puts upward pressure on wage growth, but this effect has become weaker than in the pre-2008 period, implying a flattening of the wage-unemployment relationship after accounting for structural changes. - Downward pressure on wages for individuals in occupations exposed to automation and offshoring. - Downward pressure on wages in industries with higher concentration of large firms (consistent with monopsony power concerns). - College-educated workers in routinizable jobs and in more concentrated industries face additional downward pressure; less-educated workers face a wage discount when employed in offshorable tasks. - Multiple factors (technology, globalization, market concentration) jointly contribute to weak wage growth, complicating identification of a single clear-cut explanation. ### Macro analysis — long-run determinants and cointegration evidence - Economic theory: long-run nominal wage growth determined by labor productivity growth plus price inflation. - Empirical strategy: Johansen’s (1988, 1991) maximum-likelihood procedure for a finite-order VAR using annualized log differences of quarterly level data. - Variables in VAR: growth rates of ECI for compensation in nonfarm business (∆w_t), PCE price index (∆p_t), and real output per hour in nonfarm business (∆y_t). - Sample: VAR estimated over 1990Q1-2017Q3. - Treatment: growth rates treated as individually non-stationary and integrated of order one, I(1); formal testing supports this treatment. - Johansen trace eigenvalue statistic: - Strongly rejects the null hypothesis of no cointegration in favor of at least one cointegrating relationship. - Cannot reject, at conventional significance levels, the null hypothesis of at most one relationship in favor of more than one. - Evidence points to a unique cointegrating vector. - Estimated cointegrating relationship: coefficients on inflation (∆p_t) and labor productivity growth (∆y_t) have the right signs and are statistically significant; numerically each close to minus unity. - Likelihood ratio tests do not reject the null hypothesis that the coefficients are equal to minus one, both individually and jointly. ### Final long-run representation (restricted) - Imposed restriction yields the final long-run equation reproduced from the analysis: - ∆푤ₜ = −0.9 + ∆푝ₜ + ∆푦ₜ - Interpretation: - In the long run, wage inflation increases with price inflation and labor productivity growth. - The negative and statistically significant constant (−0.9) captures the secular decline in the labor share of income over 1990-2017 and reflects that wages have fallen short of the sum of productivity and inflation growth over the period. - Industry- and state-level analysis (Abdih and Danninger (2017), as reported) attributes most of the labor-share fall to technological changes linked to automation of routine tasks, followed by trade globalization; declines in unionization also contributed. ### Stationarity tests and additional cointegration diagnostics - Multivariate stationarity tests (Johansen 1995) strongly reject the stationarity of ECI growth, inflation, and productivity growth (p-values effectively zero). - Tests preclude the presence of a stationary linear combination of the variables in levels. - Graphical evidence (w_t − p_t − y_t) shows a downward trending, apparently nonstationary series; multivariate tests confirm rejection of stationarity. ### Organization of the paper (as provided) - Section II: Macro-econometric analysis of U.S. wages and robustness checks. - Section III: Micro-econometric exercises at the individual level. - Final section: Summary of key messages and concluding remarks. *Source: wp18138 (excerpt from working paper PDF, content pages including INTRODUCTION and MACRO ANALYSIS).* ### 14.5 with a p value of 0.0007. In ### wp18138 - 14.5 with a p value of 0.0007. In ### Cointegration and the Long Run - Variables in levels do not cointegrate (contextual contrast stated). - Variables in growth rates cointegrate into the stationary linear combination of equation 1. - Empirical evidence: - The series ∆w_t +0.9 − ∆p_t − ∆y_t exhibits mean reversion (Figure 3). - Augmenting the VAR with the Congressional Budget Office’s (CBO) unemployment gap yields evidence of one and only one cointegrating vector. - The coefficient on the unemployment gap in the cointegrating vector is numerically very small and statistically indistinguishable from zero: Chi^2(1) = 0.77 [0.381]. - The cointegrating relationship in equation 1 continues to hold when including the unemployment gap. ### Role of Labor Market Slack - Conceptually, labor market slack should not affect wage growth in the long run. - Empirical finding: slack (CBO unemployment gap) does not affect the long-run cointegrating relationship but can matter in the short run. ### Short Run: Estimation Strategy and ADL Model - Two-step approach: 1. Estimate trend wage growth using the cointegrating relationship in equation 1. - Trend inflation (∆p_t^trend) measured by expected long run (10 yr.) PCE inflation from the Survey of Professional Forecasters (SPF). - Trend labor productivity growth (∆y_t^trend) constructed via Baxter and King (1999) filter using Staiger, Stock, and Watson (2001) filter width and cutoffs. 2. Model the deviation of actual wage growth from trend (the wage growth gap) as a function of the unemployment gap in an autoregressive distributed lag (ADL) model. - Initial ADL specification: - Wage growth gap regressed on its own 8 lags and the current value plus 8 lags of the unemployment gap (Ugap_t), where Ugap_t = actual unemployment − CBO natural rate. - Empirical simplifications: - None of the lags on the wage growth gap were statistically significant. - Lags on the unemployment gap beyond the first did not matter. - Joint zero coefficient restrictions: F(15,93) = 1.076 [0.389]. - Final ADL specification (as presented): - Equation 2 (in deviation form): - ∆w_t − ∆p_t^trend − ∆y_t^trend = θ + ∑_{s=0}^{4} λ_s (U_{t−s} − U*_ {t−s}) + ε_t - Equivalently, equation 3 (wage growth form): - ∆w_t = θ + ∆p_t^trend + ∆y_t^trend + ∑_{s=0}^{4} λ_s Ugap_{t−s} + ε_t - Interpretation: short-run deviations of wage inflation from trend depend on contemporaneous and short-lagged unemployment gap terms. ### Alternative Approach — General Unrestricted Wage Phillips Curve and Model Reduction - Start with general unrestricted dynamic model (equation 4): - ∆w_t = θ + β_1 ∆p_t^trend + β_2 ∆y_t^trend + ∑_ρ ρ_j ∆w_{t−j} + ∑_μ μ_j ∆p_{t−j} + ∑_λ λ_j Ugap_{t−j} + α (w−p−y)_{t−1} + ε_t - This general specification nests micro-founded wage Phillips curve models and allows inertia, forward-looking behavior, backward indexation, trend productivity, and a potential error-correction term. - Estimation and reduction results: - Estimated with 8 lags on wage growth, inflation, and unemployment gap (EQ(a)). - Tests support model simplification to a parsimonious specification (EQ(g)). - Key model-reduction test outcomes (sample 1990Q1-2017Q3): - EQ(a) → EQ(b): F(12,82) = 0.650 [0.7934] - EQ(b) → EQ(c): F(4,94) = 0.979 [0.4228] - EQ(a) → EQ(c): F(16,82) = 0.721 [0.7649] - (Full list of pairwise F tests provided in Table 2 with associated p-values.) - Specific restrictions validated: - Coefficients on lags 5 through 8 on all variables jointly zero: realized F = 0.65 p-value = 0.793. - Coefficients on the 4 remaining lags of ECI growth (ρ_j) jointly zero. - Coefficients on the 4 remaining lags of price inflation (μ_j) jointly zero. - Coefficient on the error correction term (α) is zero (consistent with multivariate analysis showing non-stationarity of that term). - Lags beyond the first on the unemployment gap (λ_j) not statistically significant. - Imposing these restrictions yields EQ(g), which corresponds to equation 3. ### Baseline Model Properties and Key Messages - Final (baseline) model corresponds to equation 3 and the right-hand block of Table 3. - Main economic features: - Negative and highly statistically significant constant term (headwinds to wage growth) of about one percent, attributed to secular decline in the labor share of income and drivers of technological progress and trade globalization. - The slope of the wage Phillips curve equals the sum of coefficients on current and lagged unemployment gap; it is negative and highly statistically significant. - Estimated short-run labor market sensitivity: - A one percentage point reduction in the unemployment gap implies, on average, a 0.311 percentage point increase in wage growth. - Table 3 reported parameter estimates and diagnostics (estimation sample 1990Q1-2017Q3): - Selected parameter estimates and statistics (as reported): - Coefficient blocks (left / right block formatting in source). Representative reported values: - -1.100 0.086 -12.80 0.0000 - -0.802 0.261 -3.07 0.0027 - 0.491 0.261 1.88 0.0632 - R-squared : 0.496 - S.E. of regression: 0.778 (reported) and 0.786 (other block) - Estimation sample: 1990Q1-2017Q3 - Final model diagnostics and solved cumulative impact equation: - Parameter rows reported (selected values in source): - -1.127 0.633 -1.78 0.0780 and -1.100 0.086 -12.80 0.000 - -0.311 0.051 -6.13 0.0000 and -0.311 0.050 -6.27 0.0000 - 1.017 0.152 6.69 0.0000 - 0.993 0.192 5.18 0.0000 - Testing restrictions: Chi^2(2) = 0.020637 [0.9897] - Summary quantitative takeaway: - The estimated short-run elasticity (cumulative impact) of wage growth to the unemployment gap is approximately -0.311 (i.e., a one percentage point tightening of the unemployment gap raises wage growth by 0.311 percentage points). *Source: Authors' Estimation and tables and figures as reported in the supplied content.* ### 0.280 and Yellen’s (2017) estimate of -0.333—both for the U.S. economy—and IMF’s ### wp18138 - 0.280 and Yellen’s (2017) estimate of -0.333—both for the U.S. economy—and IMF’s ### Model performance and parameter stability - Baseline model: “statistically well-behaved,” with a reasonably good fit and pseudo out-of-sample forecasts tracking realized data. - Residual diagnostics: residuals look stationary; formal tests do not reject serial uncorrelation, homoscedasticity, and normality; no evidence of an ARCH process. - Recursive estimation: parameters display remarkable stability over time; recursively estimated chow tests normalized by the one percent critical value do not reject parameter constancy. - Implication: parameter stability provides evidence against the hypothesis that the global financial crisis made the wage Phillips curve flatter. ### Decomposition of ECI growth (baseline) - Decomposition drivers (Figure 6): Inflation Expectations, Trend Productivity, Constant (other headwinds), Slack, Other. - Historical contributions since 2000: - High labor market slack during the great recession and moderating productivity growth weighed on wage growth. - Rising labor utilization during recovery exerted upward pressure on compensation growth, offset by declining contribution from productivity growth and negative contribution from the constant term. - Interpretation: augmenting the wage Phillips curve with labor productivity growth resolves the “missing” wage growth — wages are where they should be. ### Robustness: alternative measures of slack - Alternative slack concepts examined: U6 (broad unemployment measure) and UST (short-term unemployment, unemployed 26 weeks or less). - Estimation of natural rates for U6 and UST: linear transformation of CBO’s natural rate for U3 via an ADL model linking U6 (or UST) to lagged U6 (UST) and current/lagged U3; long-run coefficient on U3 used to map CBO U3 natural rate into U6/UST natural rates. - Figure 7: by U3, U6, or UST gap measures, the economy is at or beyond full employment in recent readings. - Table 4 key comparative estimates (estimation sample 1990Q1-2017Q3; U6 available from 1996Q1): - Baseline model cumulative impact (sum of unemployment gap coefficients): -0.311 (Est.s.e. 0.050, t-value -6.27, t-prob 0.000). - U6 model cumulative impact: -0.181 (Est.s.e. 0.029, t-value -6.14, t-prob 0.000). - UST model cumulative impact (reported as memo; also shows larger short-run slope): -1.135 (Est.s.e. 0.103, t-value -10.97, t-prob 0.000) and reported block shows -0.661 for a coefficient with Est.s.e. 0.114 (t-value -5.83, t-prob 0.000); cumulative impact for UST with lagged dependent variable about 0.82 in narrative (table reports -1.135 as memo cumulative). - R-squared: Baseline 0.496; U6 0.469; UST 0.490. - S.E. of regression: Baseline 0.778; U6 0.797; UST 0.783. - Interpretation: as slack is broadened (U3 → U6 → UST), sample variance of the gap increases, covariance with wage growth increases more slowly, so the ratio (slope) falls; contributions of slack to ECI growth change little across slack concepts because broader measures get smaller weights. ### Nonlinearities and Kalman filter natural rate - Nonlinearity test (quadratic unemployment gap, Table 5): coefficient on squared headline unemployment gap imprecisely estimated; null of linearity cannot be rejected; nonlinear model reduces statistically to baseline. - Kalman filter estimate of natural rate: - Natural rate modeled as random walk and jointly estimated with augmented Phillips curve. - Comparison (Figure 9a): Kalman filter natural rate and CBO series display very similar behavior; CBO series noticeably higher over 2009–14 but maximum difference about 0.3 percentage points. - Recent readings: both series put the natural rate below 4.8 percent. - Gap measures (Figure 9b) co-move closely. - Phillips curve coefficient estimates using Kalman-filter natural rate are very similar in size, sign, and statistical significance to baseline model (Table 5 right panel vs left panel). ### Alternative wage measures (macro robustness) - Alternative wage series used: ECI for wages and salaries (no employer costs for employee benefits), average hourly earnings of production and nonsupervisory employees on private nonfarm payrolls, compensation per hour in nonfarm business sector, Atlanta Fed wage tracker. - Table 6a (Johansen cointegration): tests reveal one and only one cointegrating relationship for all models — nominal wage growth depends on inflation and productivity growth with coefficient of unity on each (identical long-run result to baseline using ECI for compensation). - Short-run dynamics (Table 6b): lagged dependent variable matters in these specifications, yielding larger cumulative impacts of slack on wage growth: - Reported cumulative effects range from -0.372 to -0.557 (text). - Comparisons: Gordon (1998) estimate -0.43 using ECI wages and salaries; Staiger, Stock, and Watson (2001) state-level regressions yield -0.526 for average hourly earnings — comparable to paper’s estimates (e.g., -0.372 and -0.482 reported for some measures). ### Micro analysis: structural and cyclical determinants of U.S. wages - Data and scope: - Micro analysis uses CPS March sample 1997–2017. - Canonical Mincerian log-earnings model augmented with: local labor market slack, routinization index, offshorability index, industry employment concentration (share of workers in large firms, 500+ employees), controls for education, experience, gender, race, marital status, union status, firm size, price level, state fixed effects, year fixed effects. - State-level unemployment gap defined as ugap_rt = u_rt - û_rt where û_rt is average U.S. state unemployment rate during 2000-2005. - Structural indices: - Routinization Score: occupation-specific propensity to automate routine tasks, constructed as in prior work using 2001 O*NET values (weighted average across dimensions). - Offshorability Score: occupation’s potential to be offshored (2001 O*NET values). - Employment concentration: share of workers in two-digit industry employed in firms with 500+ employees (time-varying sectoral variable from CPS ASEC). - Correlations: routinization and offshorability weakly correlated across education groups; high-school grads moderately more routinizable; offshorable occupations slightly more common among college graduates. ### Empirical strategy and principal micro results (Table 7) - Baseline panel regression: log hourly wage on controls, local unemployment gap, routinization, offshorability, employment concentration; interactions of structural variables with education groups explored. - Sample sizes and fit: - Observations: 164,478 (full sample 1997-2017); pre-GFC and post-GFC subsamples also reported (e.g., 89,424; 53,527). - R-squared (various columns): around 0.418 to 0.4234 depending on specification. - Main findings (direct effects, full sample 1997-2017): - Routinization index: coefficient -0.0021* (standard error 0.0011) in column (1); small negative effect overall. - Offshorability index: coefficient -0.0402*** (standard error 0.0012) — occupation offshorability reduces wages by 4.02 percent holding controls constant. - Employment concentration: coefficient -0.2662*** (standard error 0.0073) — interpretation in text: a rise of the concentration ratio by 0.1 points (10 percentage points more concentrated industry) associated with a wage penalty of 2.7 percent (text clarifies the mapping from table coefficient to percent effect). - Direct effect variable (top of table) reported as 0.2266***, 0.3536***, 0.5680*** in different columns (table layout indicates multiple reported coefficients for direct effect across specifications). - Interaction results (columns 4, 4HS, 4SC, 4C+): - Routinization affects mainly skilled (college+) workers: for college+ a penalty of -5.9 percent for a 1 standard deviation higher routinization score (column 4C+ reported as -0.0589***). - Offshorability: lower-skill groups bear larger penalty; combined direct and interaction effects for lower skill ≈ -5.2 percent; skilled workers net out better (+3.2 percent = -5.2 direct + 8.4 interaction). - Employment concentration: being in a sector with 10 percentage points higher share of large employers reduces wages by 3.7 percent for the skilled relative to 1.5 percent for lower-skill workers (columns 4C+ and 4HS reported as -0.3745*** and -0.1525*** respectively). - Interpretation: international factors, technological change, and market concentration each negatively affect wages; individual effects range between about -1 to -7 percent but can sum to economically meaningful impacts; technological change and market power appear to play larger roles for skilled workers. ### Micro robustness checks (Table 8 and related) - Robustness dimensions: restrict to full-time workers; restrict to males; add industry-level openness/import competition controls; sample of workers with consecutive-year observations to examine wage growth and churning. - Results summary (Table 8): - Model 1 (All): Routinization -0.0078** (0.0032); Offshorability -0.0522*** (0.0035); Employment concentration -0.0859*** (0.0182); Observations 164,478; R-squared 0.4234. - Model 2 (Full time): Routinization -0.0112**; Offshorability -0.0830***; Employment concentration -0.0571**; Observations 108,501; R-squared 0.3650. - Model 3 (Men): Offshorability -0.0830***; Employment concentration -0.1304***; Observations 80,298; R-squared 0.4366. - Model 4 (Int’l factors added): coefficients broadly unchanged; Observations 144,980; R-squared 0.4232. - Model 5 (annual wage growth, panel of consecutive observations): structural variables retain negative signs but with smaller statistical significance; Observations 202,326; R-squared 0.0038 (noting CPS measurement noise in wage growth). - Conclusion: results largely robust to alternative sample definitions and additional controls; full-time workers appear more vulnerable to occupation-specific structural changes. ### Role of labor market slack and potential flattening of the wage Phillips curve (Table 9) - Panel wage specifications include unemployment gap (lag 12 months) and structural controls (Rout, Off, MP). - Key estimates (Table 9; dependent variable log hourly wage): - 1997-2017 (model 1): Unemp gap (lag 12m) = -0.0122*** (standard error 0.0011) — after 12 months, a one percent increase in unemployment gap lowers nominal wages by around 1.22 percent. - 1997-2007 (model 2): Unemp gap = -0.0096*** (0.0023). - 2010-2017 (model 3): Unemp gap = -0.0037 (0.0023) — effect has declined post-GFC. - Piecewise linear (kink at 5%, model 6 narrative): little evidence of a kink; pivot points between 4-6 percent cannot be rejected in pairwise comparisons at 5 percent confidence level. - Quadratic term (model 4): Unemp gap^2 (lag 12m) = 0.0003 (0.0002) — insignificant for whole period; for 1997-2007 some curvature evidence but marginal impacts not statistically different across slack ranges. - Interpretation: the wage effect of slack has fallen by more than half when comparing pre- and post-GFC periods; controlling for structural variables, the post-GFC flattening of the micro Phillips curve remains — possible contributing mechanism is a decline in voluntary labor turnover reducing reallocation and competition for jobs. ### Conclusions and overarching takeaways - Macro findings: - Productivity-augmented Phillips curve explains broad wage dynamics reasonably well. - Main macro drivers of lackluster wage growth: persistent weakening in trend labor productivity growth and secular decline in the labor share (captured by negative constant term). - Macro results robust to alternative slack and wage measures; recursive tests indicate parameter stability (no structural break at GFC). - Micro findings: - Micro-econometric analysis identifies multiple structural contributors to wage moderation: routinization (automation exposure), offshorability, and employment concentration (industry market power). - Offshorability and employment concentration have larger negative effects on wages in levels; routinization effects concentrated among college-educated workers. - The micro model suggests a significant decline in the absolute value of the wage Phillips curve slope after 2009, implying an additional labor-market related contributor to wage moderation not captured in aggregate stability tests. - Overall assessment: technology, globalization, and market power have each contributed to wage moderation; their correlated trends and causal links complicate clean decomposition of relative importance. Both macro and micro evidence imply that multiple forces together account for the prolonged modest wage growth. *Source: Authors’ estimates and analysis from the provided IMF working paper content.* ### REFERENCES ### wp18138 - REFERENCES ### Key bibliographic references - Abdih, Yasser, and Stephan Danninger, 2017. “What Explains the Decline of the U.S. Labor Share of Income? An Analysis of State and Industry Level Data,” IMF Working Paper, WP/17/167, International Monetary Fund. - Abdih, Yasser, Ravi Balakrishnan, and Baoping Shang, 2016. “What Is Keeping U.S. Core Inflation Low: Insights from a Bottom-Up Approach.” IMF Working Paper, WP/16/124, International Monetary Fund. - Acemoglu, D. 2002. Technical Change, Inequality and the Labor Market. Journal of Economic Literature 40, 7-72. - Autor, David, and Anna Salomons. 2018. “Is automation labor-displacing? 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Watson, 2001. “Prices, Wages and the U.S. NAIRU in the 1990s,” NBER Working Paper w8320. - Yellen, Janet, 2017. “Inflation, Uncertainty, and Monetary Policy,” remarks delivered at Prospects for Growth: Reassessing the Fundamentals, 59th Annual Meeting of the National Association for Business Economics, Cleveland, Ohio, September 26. ### Appendix Tables — inventory and notes - Table A1. Current Population Survey ASEC Sample 1997-2017 - Notes: Current population Survey, 1997-2017. Authors’ calculations - Table A2. Baseline regressions and results for all controls: 1997-2017 - Dependent variable: log of hourly wage rate - Source: Current Population Survey. Authors’ estimates. - Notes: All models also include state and year dummies. ### Table A2 — selected regression results (1997-2017 and subperiods) - Columns: (1) 1997-2017, (2) 1997-2007, (3) 2010-2017 - Key coefficients (coefficient (standard error)): - Unemployment gap (12 m lag): -0.0122*** (0.0011); -0.0096*** (0.0023); -0.0037 (0.0023) - Routinization index: -0.0078** (0.0032); -0.0008 (0.0040); -0.0220*** (0.0067) - Offshoreability index: -0.0522*** (0.0035); -0.0476*** (0.0044); -0.0564*** (0.0070) - Employment concentration: -0.0859*** (0.0182); -0.1289*** (0.0237); 0.0082 (0.0349) - Log CPI: 1.2062*** (0.0148); 1.3125*** (0.0268); 1.0742*** (0.0901) - High school degree: 0.2266*** (0.0086); 0.2068*** (0.0111); 0.2524*** (0.0165) - Some college: 0.3536*** (0.0089); 0.3368*** (0.0116); 0.3780*** (0.0169) - College degree: 0.5680*** (0.0112); 0.5557*** (0.0154); 0.5954*** (0.0198) - Interaction terms — Routinization & education: - High school: 0.0143*** (0.0037); 0.0087* (0.0046); 0.0256*** (0.0075) - Some college: 0.0224*** (0.0037); 0.0154*** (0.0047); 0.0382*** (0.0075) - College: -0.0589*** (0.0042); -0.0629*** (0.0055); -0.0366*** (0.0079) - Interaction terms — Offshorability & education: - High school: -0.0014 (0.0039); -0.0001 (0.0050); -0.0070 (0.0077) - Some college: 0.0064 (0.0039); 0.0106** (0.0050); 0.0014 (0.0076) - College: 0.0839*** (0.0046); 0.0720*** (0.0062); 0.1025*** (0.0084) - Interaction terms — Employment concentration & education: - High school: -0.1525*** (0.0212); -0.1054*** (0.0277); -0.2259*** (0.0401) - Some college: -0.2285*** (0.0218); -0.1890*** (0.0287); -0.2983*** (0.0408) - College: -0.3745*** (0.0267); -0.3380*** (0.0370); -0.4613*** (0.0469) - Years of potential work exp: 0.0213*** (0.0002); 0.0231*** (0.0003); 0.0197*** (0.0004) - Years of potential work exp (sqrd): -0.0004*** (0.0000); -0.0004*** (0.0000); -0.0003*** (0.0000) - Male: 0.1298*** (0.0020); 0.1449*** (0.0027); 0.1058*** (0.0034) - Caucasian: 0.0688*** (0.0025); 0.0711*** (0.0033); 0.0569*** (0.0043) - Married: 0.0837*** (0.0020); 0.0763*** (0.0027); 0.0905*** (0.0035) - Full time employment: 0.1569*** (0.0020); 0.1440*** (0.0027); 0.1731*** (0.0035) - Union: coverage: 0.2142*** (0.0028); 0.2131*** (0.0036); 0.2109*** (0.0052) - Medium-size firm: 0.0531*** (0.0039); 0.0561*** (0.0051); 0.0451*** (0.0071) - Large firm: 0.0625*** (0.0020); 0.0673*** (0.0026); 0.0515*** (0.0034) - Constant: -4.7092*** (0.0790); -5.2377*** (0.1399); -4.0142*** (0.4957) - Sample sizes and fit: - Observations: 164,478; 89,424; 53,527 - R-squared: 0.4234; 0.4069; 0.3518 *Source: wp18138 - REFERENCES (IMF Working Paper appendix).* --- _Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18138.pdf_