Over the previous quarter century, the U.S. financial system has skilled important declines in each the labor share of revenue and the pure price of curiosity, known as R*. Current analysis has largely analyzed these two developments in isolation. On this publish, we offer a easy mannequin that captures the joint evolution of the labor share and R*, which we name the R*–labor share nexus. Our key discovering is that structural modifications affecting R* additionally affect the evolution of the labor share, and thereby wages and costs. This highlights a doubtlessly essential channel, absent from many macroeconomic fashions, by means of which the components that decide R* additionally have an effect on the labor share and, in flip, broader macroeconomic developments, with implications for financial coverage.
Frequent Traits
The declines within the labor share and R* over the previous twenty-five years are evident within the chart beneath. The labor share is “the fraction of financial output that accrues to staff as compensation in alternate for his or her labor” (Giandrea and Sprague 2017). The blue line reveals the labor share within the U.S. nonfarm enterprise sector, which fluctuated between 60 and 65 p.c from 1970 to 2000, then declined to about 55 p.c in recent times. An identical sample is noticed throughout various measures of the labor share. R* is “the true rate of interest per output equaling its pure price and steady inflation” (Laubach and Williams 2003). The crimson line reveals estimates of U.S. R* from the Holston–Laubach–Williams (HLW) mannequin (Holston et al. 2017; Holston et al. 2023), which fluctuated between 2½ and 4 p.c from 1970 to 2000, then declined to about 1 p.c in recent times.
Parallel Motion of the Labor Share and R*
Notice: This chart plots the labor share of revenue within the U.S. nonfarm enterprise sector and estimates of the U.S. pure price of curiosity, R*, from the Holston–Laubach–Williams (HLW) mannequin, from 1970:Q1 to 2025:This fall.
A putting characteristic of the above chart is the shut parallel motion of the labor share and R* over time. Nonetheless, this visible similarity ought to be interpreted with warning. Many unrelated information sequence exhibit comparable tendencies over stretches of time, so the discovering that two sequence look alike might merely mirror random probability. As well as, one ought to heed the adage that “correlation doesn’t suggest causation”: the labor share and R* is probably not immediately linked, however moderately collectively influenced by different components. To handle these points, researchers flip to financial concept and statistical strategies to higher perceive the sources and nature of correlations over time.
Let Concept Be the Information
Financial concept can present insights into the correlation between the labor share and R* by figuring out components that affect each. A big literature has examined the determinants of the labor share, together with modifications in know-how and productiveness, demographics, corporations’ market energy in worth setting, globalization, and measurement points (Karabarbounis and Neiman 2014; Charpe et al. 2020; Grossman et al. 2021; Acemoglu and Restrepo 2022; Eggertsson et al. 2021; Velasquez 2023; Elsby et al. 2013; Grossman and Oberfield 2022). A separate literature has examined the determinants of R*. Laubach and Williams (2003) and Holston et al. (2017) emphasize the constructive relationship between progress and R* implied by the everlasting revenue speculation, whereas Carvalho et al. (2016), Mian et al. (2021), Auclert et al. (2025), and Carvalho et al. (2025) spotlight a adverse relationship between life expectancy and R*. Eggertsson et al. (2019) and Rachel (2025) analyze extra complicated fashions that permit for extra influences on R*, together with modifications in know-how, market energy, international components, fiscal coverage, and the labor share. Bom et al. (2005) additionally hypothesize that R* is dependent upon the labor share.
Taken collectively, these two literatures recommend that widespread components might have an effect on the labor share and R* in the identical path, offering a possible theoretical hyperlink between the 2. For instance, the mannequin of Grossman et al. (2021) predicts that the labor share is positively associated to the speed of productiveness progress and negatively associated to life expectancy. This constructive longer-run relationship between progress and the labor share is supported by proof in Charpe et al. (2020). The literature on R* yields the identical qualitative predictions for a way progress and life expectancy have an effect on R*. On the similar time, one mustn’t anticipate the correlation between the labor share and R* to be actual, as every could also be affected by extra idiosyncratic components. These concerns information the empirical evaluation that follows.
From Concept to Proof
Constructing on financial concept, we hypothesize that the labor share and R* are collectively decided, whereas permitting for idiosyncratic components that have an effect on every individually. All through the empirical evaluation, we use the pure logarithm of the nonfarm enterprise labor share index from the Bureau of Labor Statistics. We measure R* utilizing HLW estimates as of 2025:This fall. Notice that HLW estimates of R* encompass two parts: the estimated development progress price of the financial system and an unobserved variable that displays influences on R* past development progress.
We start by testing for a longer-run relationship between the labor share and R* utilizing cointegration, a typical statistical technique for analyzing relationships between nonstationary variables—that’s, variables that don’t revert to a relentless imply over time. The outcomes point out sturdy proof of a cointegrating relationship between the labor share and R*, implying {that a} linear mixture of those two time sequence reveals a steady and bounded longer-run relationship. Subsequent, we take a look at for a longer-run relationship between the labor share and solely the development progress part of R*, however we don’t discover equally sturdy proof. This implies that the opposite part of R*, which displays influences past development progress, additionally performs an essential position in explaining the sturdy relationship between the labor share and R*.
Based mostly on this statistical evaluation, we posit a easy mannequin of the labor share, through which the development labor share is dependent upon R* and a relentless, and the precise labor share adjusts towards this development worth over time. Particularly, the development labor share, denoted S*, is given by S* = αR* + θ. Every quarter, the labor share closes a portion ρ of the hole between its precise and development values.
The primary column of the desk beneath stories the mannequin’s parameter estimates for the pattern 1970–2025, which we check with because the baseline specification. The estimate of α implies {that a} 1 proportion level improve in R* is related to a 0.044 improve within the (log) development labor share. Evaluated on the pattern common labor share of 60 p.c, this corresponds to roughly a 2½ proportion level improve within the development labor share. The estimate of ρ implies that it takes about three quarters for half of the hole between the precise and development labor share to shut.
Labor Share Mannequin Parameter Estimates
| Pattern | |||||
| Parameter | 1970–2025 | 1970–2025 with time development |
1970–2005 | 1970–2015 | 1965–2025 |
| α | 0.044 (0.003) |
0.038 (0.005) |
0.038 (0.007) |
0.040 (0.002) |
0.040 (0.004) |
| θ | 4.549 (0.007) |
4.565 (0.013) |
4.568 (0.022) |
4.562 (0.008) |
4.555 (0.011) |
| ρ | 0.222 (0.034) |
0.240 (0.037) |
0.216 (0.042) |
0.269 (0.038) |
0.143 (0.027) |
| τ | – | 0.000 (0.000) |
– | – | – |
| S.E. of regression | 0.009 | 0.009 | 0.008 | 0.009 | 0.009 |
Notes: This desk stories parameter estimates from a number of specs of our labor share mannequin, through which the development labor share is given by S* = αR* + θ, and every quarter, the labor share closes a portion ρ of the hole between its precise and development values. The primary column stories estimates for the pattern 1970–2025 (baseline specification). The second column stories estimates for the pattern 1970–2025 together with a time development with parameter τ. The third by means of fifth columns report estimates for various samples 1970–2005, 1970–2015, and 1965–2025. Commonplace errors are in parentheses. The underside row stories the usual error of every regression.
The chart beneath reveals that the mannequin’s dynamic forecast of the labor share (crimson line)—primarily based solely on R* and the mannequin’s parameter estimates—tracks the precise labor share (blue line) properly, capturing each longer-run tendencies and short-term fluctuations.
Dynamic Forecasts of the Labor Share
Notes: This chart plots the pure logarithm of the nonfarm enterprise labor share index and our mannequin’s dynamic forecasts of the labor share beneath the baseline (fixed θ) and time-varying θ specs, from 1970:Q1 to 2025:This fall. The forecasts are primarily based on R*, the mannequin’s parameter estimates, and—beneath the time-varying θ specification—the estimated path of θ.
These outcomes are sturdy to modifications within the mannequin specification, corresponding to together with a time development and utilizing various samples, offering additional help that the connection between the labor share and R* is just not spurious. The second column of the above desk stories parameter estimates from a specification that features a time development within the development labor share. The estimated parameter on the time development, denoted τ, is statistically insignificant, and the estimate of α—which measures the energy of the connection between R* and the development labor share—is just modestly smaller than within the baseline specification. This means that the connection between the labor share and R* is just not merely the results of each having downward tendencies over the pattern. The third by means of fifth columns of the above desk report parameter estimates for various samples. The estimates of α are fairly comparable throughout samples, no matter whether or not they embody the interval of sharp decline within the labor share following the 2007–2009 recession.
Up so far, by assuming that θ is fixed, we’ve successfully assumed that R* is the one issue influencing the development labor share. We now chill out this assumption by permitting θ to range over time, capturing extra influences on the development labor share past R*. We let θ observe a random stroll and estimate it utilizing the Kalman filter. The gold line within the above chart reveals the mannequin’s dynamic forecast of the labor share beneath this time-varying θ specification. Permitting for time-varying θ solely modestly improves the mannequin’s match to the info relative to the baseline (fixed θ) specification, and the ensuing forecast doesn’t differ meaningfully from the baseline forecast. This implies that when the connection between R* and the labor share is accounted for, different components have had comparatively little internet impact on the labor share over the pattern.
Financial Coverage Implications
Our outcomes point out that a lot of the variation within the labor share will be accounted for by actions in R*. This R*–labor share nexus means that structural modifications within the financial surroundings that have an effect on R*—corresponding to shifts in productiveness progress or demographics—might have broader implications for wages and costs than is often assumed in macroeconomic fashions that deal with the labor share as fixed. Accordingly, one ought to take into consideration the joint willpower of R* and the labor share when analyzing the macroeconomic results and financial coverage implications of modifications within the components that affect R*. For instance, future durations of very low R* are more likely to be accompanied by low ranges of the labor share, whereas will increase within the development progress price of the financial system might enhance each R* and the labor share.
Sophia Cho is a analysis analyst within the Federal Reserve Financial institution of New York’s Analysis and Statistics Group.
John C. Williams is the president and chief government officer of the Federal Reserve Financial institution of New York.
Tips on how to cite this publish:
Sophia Cho and John C. Williams, “The R*–Labor Share Nexus,” Federal Reserve Financial institution of New York Liberty Road Economics, April 15, 2026, https://doi.org/10.59576/lse.20260415
BibTeX: View |
Disclaimer
The views expressed on this publish are these of the creator(s) and don’t essentially mirror the place of the Federal Reserve Financial institution of New York or the Federal Reserve System. Any errors or omissions are the duty of the creator(s).
