Wage growth and labor market tightness

Layer 1 — Overview

Research Question. Which measures of labor market tightness best predict nominal wage inflation, and do standard measures such as the unemployment rate and the vacancy-to-unemployment ratio capture the relevant slack? The paper also asks whether transitory productivity shocks affect wage growth, and whether the wage Phillips curve is nonlinear.

Motivation and Model. Standard measures of labor market tightness have had mixed performance since the COVID-19 pandemic: unemployment quickly returned to pre-pandemic levels while wage growth remained persistently elevated, motivating a search for superior indicators. The paper builds on the theoretical framework of Bloesch, Lee, and Weber (2024), a tractable New Keynesian DSGE model in which firms set wages and workers search on the job. In this model, labor market tightness is well-summarized by either (a) the quits rate or (b) vacancies per effective searcher (V/ES), where effective searchers include both employed and unemployed job seekers. Unemployment enters the model’s wage Phillips curve but with a coefficient close to zero, because changes in the unemployment share do not substantially shift the composition of searchers in a way that alters firms’ wage incentives. Transitory TFP shocks have theoretically ambiguous effects on nominal wage growth because the outcome depends on the central bank’s policy response.

Data and Methods. The main analysis uses quarterly U.S. data from 1990:Q2 to 2024:Q2. Wage growth is measured as the 3-month log change in the Employment Cost Index (ECI) for wages and salaries of private industry workers. Quits and vacancies are drawn from JOLTS (2001:Q1 forward) and extended back to 1990:Q2 using the Davis-Faberman-Haltiwanger series and Barnichon’s composite Help Wanted Index, respectively. The authors run a “horse race” of OLS univariate regressions of wage growth on thirteen separately normalized tightness indicators. They then run bivariate regressions pairing the quits rate with each other indicator to test whether any alternative provides independent predictive power. Robustness is assessed using 12-month ECI changes. An industry-level panel with time and industry fixed effects covering 11 broad sectors from JOLTS for 2001:Q1–2024:Q2 tests whether the same ranking holds within industries. Forecasting exercises use 1-, 2-, and 4-quarter-ahead in-sample regressions plus rolling out-of-sample one-quarter-ahead predictions beginning in 2004:Q1. Nonlinearity is evaluated via threshold regressions at the 25th percentile (unemployment) or 75th percentile (other measures) and via quadratic specifications.

Main Findings with Quantitative Magnitudes.

Horse race (aggregate, contemporaneous): The quits rate explains 55 percent of variation in 3-month ECI wage growth (R² = 0.55), and V/ES explains 52 percent (R² = 0.52), the two highest among all indicators tested. A one standard deviation increase in either quits (0.39 percentage points) or V/ES (0.08) is associated with 0.20 percentage points higher 3-month wage growth. By contrast, the vacancy-to-unemployment ratio (V/U) explains only 41 percent of wage growth and the unemployment rate only 34 percent. Together, quits and V/ES explain nearly two-thirds of wage growth since 1994 and 78 percent since 2020:Q2.

Bivariate regressions: Conditional on the quits rate, the coefficient on every other tightness indicator drops to near zero, with the sole exception of V/ES, which retains a coefficient of 0.08 (significant) while the quits coefficient remains at 0.14. This result is consistent with the model’s prediction that quits and V/ES are close to sufficient statistics for labor market tightness.

12-month ECI results: The ranking is preserved at longer horizons; quits and V/ES each explain approximately two-thirds of 12-month wage growth.

Productivity: Regressions of 3-month ECI wage growth on 3-month changes in labor productivity, TFP, and utilization-adjusted TFP all yield small, negative, and statistically indistinguishable from zero coefficients, consistent with the model’s prediction of an ambiguous effect of transitory productivity shocks on nominal wages.

Industry-level panel: Quits and V/ES remain the strongest predictors of within-industry wage growth after absorbing industry and time fixed effects. A one standard deviation increase in the industry quits rate (0.93 percentage points) is associated with 0.23 percentage points higher quarterly wage growth; a one standard deviation increase in industry V/ES (0.11) is associated with 0.13 percentage points higher wage growth.

HPW Composite Index: The Heise-Pearce-Weber (HPW) Index, constructed as an OLS-weighted average of quits and V/ES, achieves a correlation of 0.9 with standardized 3-month ECI wage growth. In-sample forecasting R² for the HPW Index at 1, 2, and 4 quarters ahead is 0.62, 0.74, and 0.77, respectively — the highest of all indicators at each horizon.

Out-of-sample forecasting: Only the quits rate and the HPW Index consistently outperform a simple AR(1) benchmark throughout the out-of-sample period from 2004:Q1 to 2024:Q1. The forecasting performance of vacancy-based measures (V/U and V/ES) deteriorated steadily after 2015, consistent with evidence of structural shifts in vacancy measurement documented by Mongey and Horwich (2023).

Nonlinearity: Threshold regressions and quadratic specifications provide little evidence of meaningful nonlinearity in the wage-tightness relationship for quits, V/ES, or the HPW Index over 1990–2024. The fit improvement from adding threshold terms is marginal, and slope coefficients are broadly stable across the full range of tightness, including the extreme tightness observed after COVID.

Layer 2 — Q&A

Q1: What theoretical mechanism links quits and V/ES to nominal wage growth, in contrast to unemployment?

In the Bloesch-Lee-Weber (2024) model incorporated in the paper, firms use both wages and vacancies to attract and retain workers from unemployment and from other firms, conditional on the overall mass of effective searchers. Labor market tightness is defined as V/S (vacancies over total searchers), not V/U, because employed workers also search on the job. When tightness is high, workers are harder to recruit and more likely to be poached, pressuring firms to raise wages. Quits are the endogenous component of separations and rise mechanically with tightness, making them a near-equivalent sufficient statistic for V/ES. Unemployment enters the wage Phillips curve in principle because the composition of searchers (employed vs. unemployed) matters for firms’ wage-setting incentives, but the coefficient on unemployment is calibrated and estimated to be approximately zero.

Q2: How do the authors extend the quits and vacancies data back to 1990 to cover the full sample period?

JOLTS data on quits and job openings begin in 2001:Q1. The authors extend the quits rate backward to 1990:Q2 using the Davis, Faberman, and Haltiwanger (2012) series, taking a simple average of the two in overlapping quarters (2001:Q1–2010:Q2). Vacancies are extended back to 1990:Q2 using the composite Help Wanted Index constructed by Barnichon (2010), with a similar overlapping average for 2000:Q4–2021:Q3. The effective-searcher measure (V/ES) is available only from 1994:Q1 because the CPS marginally attached worker series begins then.

Q3: How is the V/ES measure constructed, and why does it differ from the standard V/U ratio?

Effective searchers are constructed as ES = U_s + 0.48·U_l + 0.40·Z_want + 0.09·Z_do-not-want + 0.07·N, where U_s is short-term unemployed (less than 27 weeks), U_l is long-term unemployed (27+ weeks), Z_want is marginally attached workers not in the labor force, Z_do-not-want is non-participants not marginally attached, and N is employment. The weights reflect relative search intensities estimated by Abraham, Haltiwanger, and Rendell (2020) and translated to publicly available CPS data by Sahin (2020). Because employed workers constitute a far larger share of the population than the unemployed, including them — even at the low weight of 0.07 — substantially increases the total effective searcher count relative to V/U. This matters because the model predicts that firms’ wage decisions depend on the full pool of potential recruits and retention risk, not just the unemployed.

Q4: What are the results of the bivariate “horse race” pairing quits with each other tightness measure?

In bivariate OLS regressions of 3-month ECI wage growth on the quits rate plus one other indicator, the coefficient on quits remains approximately 0.14–0.22 percentage points per standard deviation regardless of which other variable is included, while all competing indicators’ coefficients fall to near zero. The sole partial exception is V/ES, which retains a coefficient of 0.08 (significant at 5%) alongside a quits coefficient of 0.14; the combined fit is 0.60. For all other measures — including V/U (coefficient drops to 0.04), unemployment (0.00), jobs-workers gap (0.02), Conference Board availability (−0.01), and NFIB difficulty hiring (0.01) — the incremental contribution beyond quits is negligible. This result is consistent with the model’s prediction that quits and V/ES are jointly near-sufficient statistics for wage growth.

Q5: Do the industry-level panel regressions replicate the aggregate ranking, and why is this an important test?

Yes. In panel regressions with industry and time fixed effects covering 11 JOLTS sectors from 2001:Q1 to 2024:Q2, the quits rate has the highest within-industry R² (0.019) and V/ES the second highest (0.010); all other indicators rank below. This within-industry test is important because it removes the possibility that the aggregate correlations are driven by unobserved macro variables that happen to co-move with quits and V/ES. The bivariate industry panel confirms that, conditional on quits, only V/ES adds substantially to the within-industry fit; all other indicators add negligible explanatory power.

Q6: Why might industry-level TFP shocks have a modest positive effect on wages even though aggregate TFP shocks do not?

At the industry level, the central bank does not respond to industry-specific TFP shocks. When a particular industry’s productivity rises and firms lower prices, consumer demand for that industry’s output rises. If demand rises by enough, firms must hire more workers to meet demand despite higher productivity per worker, leading them to post more vacancies and raise wages. At the aggregate level, the central bank does respond to the disinflation associated with positive TFP shocks (following a Taylor rule), which can raise overall consumption enough to require more aggregate hiring and generate a positive TFP-wage correlation — but the direction depends on monetary policy responsiveness, making the aggregate relationship ambiguous and empirically insignificant. The industry regressions find that a 1 percent increase in annual labor productivity is associated with 0.15 percent higher industry annual wage growth, significant at the 10 percent level.

Q7: How is the HPW Index constructed, and what is its in-sample fit with wage growth?

The HPW Index is constructed as a weighted average of the standardized quits rate and V/ES, where the weights are the OLS coefficients from a bivariate regression of 3-month ECI wage growth on both variables simultaneously (estimated over 1994:Q1–2024:Q2). The index is then normalized to have mean zero and standard deviation of one. The HPW Index achieves a correlation of 0.9 with standardized 3-month ECI wage growth. At the peak of post-pandemic inflation, the index predicted wage growth of approximately 2.6 standard deviations above the mean, corresponding to a quarterly wage growth rate of about 1.3 percent, close to realized values.

Q8: How do the out-of-sample forecasting results compare across indicators, and what accounts for the deterioration of vacancy-based measures?

Rolling out-of-sample one-quarter-ahead predictions from 2004:Q1 to 2024:Q1 show that only the quits rate and the HPW Index consistently outperform an AR(1) benchmark across the full period. V/U performed relatively well until 2015 but then deteriorated steadily, and V/ES similarly weakened after 2015, consistent with the finding by Mongey and Horwich (2023) that the relationship between job vacancies and other labor market indicators has persistently shifted since approximately 2010. The forecasting performance of the unemployment rate and several other standard measures deteriorated sharply in the post-COVID period when wage inflation surged, but quits and HPW maintained their performance throughout.

Q9: Is there evidence of nonlinearity in the wage Phillips curve, particularly in the extreme tightness of the post-COVID period?

The paper finds little evidence of meaningful nonlinearity. Threshold regressions at the 25th percentile for unemployment and 75th percentile for other measures yield marginal fit improvements: the R² for unemployment rises from 0.34 to 0.36 (a level shift rather than a slope change), and fit improvements for HPW, quits, and V/ES are essentially zero. Quadratic specifications confirm this: the coefficient on the squared term is insignificant in all specifications. The authors conclude that the relationship between labor market tightness (as measured by quits or the HPW Index) and nominal wage growth is approximately linear, including during the extreme tightness of the COVID aftermath.

Q10: Why does the paper argue that the slope of the wage Phillips curve can be estimated more cleanly than the price Phillips curve?

In the model’s price Phillips curve, monetary policy endogenously responds to TFP shocks, creating an omitted variable problem that biases the estimated slope toward zero. In the wage Phillips curve, TFP and monetary policy shocks affect wages only through their general equilibrium effects on labor market tightness — they do not appear directly on the right-hand side. Consequently, the tightness variable is a sufficient statistic for wage inflation in the model, and the slope coefficient can be estimated consistently from reduced-form regressions without the identification problems that plague the price Phillips curve.

Key Concepts

Vacancies per Effective Searcher (V/ES). The paper’s preferred tightness measure, defined as job openings divided by effective searchers, where effective searchers are ES = U_s + 0.48·U_l + 0.40·Z_want + 0.09·Z_do-not-want + 0.07·N. This differs from the standard V/U ratio by including employed workers (at a weight of 0.07 reflecting their search intensity) and distinguishing between short-term and long-term unemployed and non-participants. It is the theoretically correct tightness measure in the on-the-job-search model, where the full pool of potential recruits — not only the unemployed — determines wage pressure.

On-the-Job Search. The mechanism by which employed workers actively search for and receive job offers from other firms. In the Bloesch-Lee-Weber (2024) model underpinning the paper, on-the-job search implies that firms must set wages not only to attract unemployed workers but also to retain employed workers who may be poached. This changes the relevant measure of tightness from V/U to V/S and makes quits — which are the endogenous separations triggered when workers accept outside offers — a near-sufficient statistic for wage growth.

Quits Rate. The ratio of voluntary separations (quits) to total employment in private sector, sourced from JOLTS (extended to 1990 using Davis et al. 2012). In the model, quits are the endogenous component of the separation rate and are tightly linked to vacancies per effective searcher because workers quit more frequently when labor market tightness is high and outside offers are plentiful. The paper establishes quits as the single best individual predictor of 3-month ECI wage growth (R² = 0.55) and the best out-of-sample forecaster along with HPW.

HPW Tightness Index (Heise-Pearce-Weber Index). A composite indicator of labor market tightness constructed as the OLS-coefficient-weighted average of the quits rate and V/ES, estimated by regressing 3-month ECI wage growth on both variables simultaneously. The index is normalized to mean zero and standard deviation of one. The HPW Index achieves the highest in-sample forecasting fit at 1, 2, and 4 quarters ahead (R² of 0.62, 0.74, and 0.77, respectively) and consistently outperforms the AR(1) benchmark out of sample, unlike most other indicators.

Wage Phillips Curve. The reduced-form relationship between nominal wage inflation and labor market tightness, derived in the paper from first-order conditions of the firm’s optimization problem. In the model’s representation (equation 3), wage inflation is a function of deviations of V/ES and unemployment from steady state plus expected future wage inflation. The paper argues this relationship can be estimated more cleanly than the price Phillips curve because TFP and monetary policy shocks affect wages only through the tightness term, avoiding the omitted-variable bias that flattens price Phillips curve estimates.

Sufficient Statistic for Wage Inflation. As used in the paper’s model, a variable (or pair of variables) such that once it is included in the wage Phillips curve, no other labor market indicator provides additional explanatory power for wage growth. The model predicts, and the empirical horse race confirms, that quits or V/ES are individually near-sufficient statistics: conditional on the quits rate, the coefficients on all other tightness measures (including unemployment, V/U, jobs-workers gap, and survey measures) fall to approximately zero.

Transitory TFP Shocks and Wage Growth. The paper defines these as short-lived, positive shocks to total factor or labor productivity, as measured by 3-month changes in Fernald et al. (2012) series. The theoretical prediction is that their effect on nominal wage growth is ambiguous: if the central bank’s policy response lowers real rates enough, aggregate demand rises sufficiently to require more hiring, generating positive wage effects; if the policy response is limited, lower marginal costs reduce vacancies and wages. In the data, the sign is negative across all three productivity measures but statistically indistinguishable from zero in all specifications.