The R*–Labor Share Nexus - Liberty Street Economics

The R*–Labor Share Nexus - Liberty Street Economics
Liberty Street Economics
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April 15, 2026
The R*–Labor Share Nexus
Sophia Cho and John C. Williams
Over the past quarter century, the U.S. economy has experienced significant declines in both the labor share of income and the natural rate of interest, referred to as R*. Existing research has largely analyzed these two developments in isolation. In this post, we provide a simple model that captures the joint evolution of the labor share and R*, which we call the R*–labor share nexus. Our key finding is that structural changes affecting R* also influence the evolution of the labor share, and thereby wages and prices. This highlights a potentially important channel, absent from many macroeconomic models, through which the factors that determine R* also affect the labor share and, in turn, broader macroeconomic developments, with implications for monetary policy.
Common Trends
The declines in the labor share and R* over the past twenty-five years are evident in the chart below. The labor share is “the fraction of economic output that accrues to workers as compensation in exchange for their labor” (
Giandrea and Sprague 2017
). The blue line shows the labor share in the U.S. nonfarm business sector, which fluctuated between 60 and 65 percent from 1970 to 2000, then declined to about 55 percent in recent years. A similar pattern is observed across alternative measures of the labor share. R* is “the real interest rate consistent with output equaling its natural rate and stable inflation” (
Laubach and Williams 2003
). The red line shows estimates of U.S. R* from the Holston–Laubach–Williams (HLW) model (
Holston et al. 2017
Holston et al. 2023
), which fluctuated between 2½ and 4 percent from 1970 to 2000, then declined to about 1 percent in recent years.
Parallel Movement of the Labor Share and R*
Percent
Percent
Sources: Haver Analytics; authors’ calculations.
Note: This chart plots the labor share of income in the U.S. nonfarm business sector and estimates of the U.S. natural rate of interest, R*, from the Holston–Laubach–Williams (HLW) model, from 1970:Q1 to 2025:Q4.
A striking feature of the above chart is the close parallel movement of the labor share and R* over time. However, this visual similarity should be interpreted with caution. Many unrelated data series exhibit similar trends over stretches of time, so the finding that two series look alike may merely reflect random chance. In addition, one should heed the adage that “correlation does not imply causation”: the labor share and R* may not be directly connected, but rather jointly influenced by other factors. To address these issues, researchers turn to economic theory and statistical methods to better understand the sources and nature of correlations over time.
Let Theory Be the Guide
Economic theory can provide insights into the correlation between the labor share and R* by identifying factors that influence both. A large literature has examined the determinants of the labor share, including changes in technology and productivity, demographics, firms’ market power in price setting, globalization, and measurement issues (
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 positive relationship between growth and R* implied by the permanent income hypothesis, while
Carvalho et al. (2016)
Mian et al. (2021)
Auclert et al. (2025)
, and
Carvalho et al. (2025)
highlight a negative relationship between life expectancy and R*.
Eggertsson et al. (2019)
and
Rachel (2025)
analyze more complex models that allow for additional influences on R*, including changes in technology, market power, global factors, fiscal policy, and the labor share.
Bom et al. (2005)
also hypothesize that R* depends on the labor share.
Taken together, these two literatures suggest that common factors may affect the labor share and R* in the same direction, providing a potential theoretical link between the two. For example, the model of
Grossman et al. (2021)
predicts that the labor share is positively related to the rate of productivity growth and negatively related to life expectancy. This positive longer-run relationship between growth and the labor share is supported by evidence in
Charpe et al. (2020)
. The literature on R* yields the same qualitative predictions for how growth and life expectancy affect R*. At the same time, one should not expect the correlation between the labor share and R* to be exact, as each may be affected by additional idiosyncratic factors. These considerations guide the empirical analysis that follows.
From Theory to Evidence
Building on economic theory, we hypothesize that the labor share and R* are jointly determined, while allowing for idiosyncratic factors that affect each separately. Throughout the empirical analysis, we use the natural logarithm of the nonfarm business labor share index from the Bureau of Labor Statistics. We measure R* using HLW estimates as of 2025:Q4. Note that HLW estimates of R* consist of two components: the estimated trend growth rate of the economy and an unobserved variable that reflects influences on R* beyond trend growth.
We begin by testing for a longer-run relationship between the labor share and R* using cointegration, a standard statistical method for analyzing relationships between nonstationary variables—that is, variables that do not revert to a constant mean over time. The results indicate strong evidence of a cointegrating relationship between the labor share and R*, implying that a linear combination of these two time series exhibits a stable and bounded longer-run relationship. Next, we test for a longer-run relationship between the labor share and only the trend growth component of R*, but we do not find similarly strong evidence. This suggests that the other component of R*, which reflects influences beyond trend growth, also plays an important role in explaining the strong relationship between the labor share and R*.
Based on this statistical analysis, we posit a simple model of the labor share, in which the trend labor share depends on R* and a constant, and the actual labor share adjusts toward this trend value over time. Specifically, the trend labor share, denoted S*, is given by S* = αR* + θ. Each quarter, the labor share closes a portion ρ of the gap between its actual and trend values.
The first column of the table below reports the model’s parameter estimates for the sample 1970–2025, which we refer to as the baseline specification. The estimate of α implies that a 1 percentage point increase in R* is associated with a 0.044 increase in the (log) trend labor share. Evaluated at the sample average labor share of 60 percent, this corresponds to approximately a 2½ percentage point increase in the trend labor share. The estimate of ρ implies that it takes about three quarters for half of the gap between the actual and trend labor share to close.
Labor Share Model Parameter Estimates
Sample
Parameter
1970–2025
1970–2025
with time trend
1970–2005
1970–2015
1965–2025
0.044
(0.003)
0.038
(0.005)
0.038
(0.007)
0.040
(0.002)
0.040
(0.004)
4.549
(0.007)
4.565
(0.013)
4.568
(0.022)
4.562
(0.008)
4.555
(0.011)
0.222
(0.034)
0.240
(0.037)
0.216
(0.042)
0.269
(0.038)
0.143
(0.027)
0.000
(0.000)
S.E. of regression
0.009
0.009
0.008
0.009
0.009
Source: Authors’ calculations.
Notes: This table reports parameter estimates from several specifications of our labor share model, in which the trend labor share is given by S* = αR* + θ, and each quarter, the labor share closes a portion ρ of the gap between its actual and trend values. The first column reports estimates for the sample 1970–2025 (baseline specification). The second column reports estimates for the sample 1970–2025 including a time trend with parameter τ. The third through fifth columns report estimates for alternative samples 1970–2005, 1970–2015, and 1965–2025. Standard errors are in parentheses. The bottom row reports the standard error of each regression.
The chart below shows that the model’s dynamic forecast of the labor share (red line)—based solely on R* and the model’s parameter estimates—tracks the actual labor share (blue line) well, capturing both longer-run trends and short-term fluctuations.
Dynamic Forecasts of the Labor Share
Log labor share index
Sources: Haver Analytics; authors’ calculations.
Notes: This chart plots the natural logarithm of the nonfarm business labor share index and our model’s dynamic forecasts of the labor share under the baseline (constant θ) and time-varying θ specifications, from 1970:Q1 to 2025:Q4. The forecasts are based on R*, the model’s parameter estimates, and—under the time-varying θ specification—the estimated path of θ.
These results are robust to modifications in the model specification, such as including a time trend and using alternative samples, providing further support that the relationship between the labor share and R* is not spurious. The second column of the above table reports parameter estimates from a specification that includes a time trend in the trend labor share. The estimated parameter on the time trend, denoted τ, is statistically insignificant, and the estimate of α—which measures the strength of the relationship between R* and the trend labor share—is only modestly smaller than in the baseline specification. This indicates that the relationship between the labor share and R* is not merely the result of both having downward trends over the sample. The third through fifth columns of the above table report parameter estimates for alternative samples. The estimates of α are quite similar across samples, regardless of whether they include the period of sharp decline in the labor share following the 2007–2009 recession.
Up to this point, by assuming that θ is constant, we have effectively assumed that R* is the only factor influencing the trend labor share. We now relax this assumption by allowing θ to vary over time, capturing additional influences on the trend labor share beyond R*. We let θ follow a random walk and estimate it using the Kalman filter. The gold line in the above chart shows the model’s dynamic forecast of the labor share under this time-varying θ specification. Allowing for time-varying θ only modestly improves the model’s fit to the data relative to the baseline (constant θ) specification, and the resulting forecast does not differ meaningfully from the baseline forecast. This suggests that once the relationship between R* and the labor share is accounted for, other factors have had relatively little net effect on the labor share over the sample.
Monetary Policy Implications
Our results indicate that much of the variation in the labor share can be accounted for by movements in R*. This R*–labor share nexus suggests that structural changes in the economic environment that affect R*—such as shifts in productivity growth or demographics—may have broader implications for wages and prices than is typically assumed in macroeconomic models that treat the labor share as constant. Accordingly, one should take into account the joint determination of R* and the labor share when analyzing the macroeconomic effects and monetary policy implications of changes in the factors that influence R*. For example, future periods of very low R* are likely to be accompanied by low levels of the labor share, while increases in the trend growth rate of the economy may boost both R* and the labor share.
Sophia Cho is a research analyst in the Federal Reserve Bank of New York’s Research and Statistics Group.
John C. Williams
is the president and chief executive officer of the Federal Reserve Bank of New York.
How to cite this post:
Sophia Cho and John C. Williams, “The R*–Labor Share Nexus,” Federal Reserve Bank of New York
Liberty Street Economics
, April 15, 2026,
BibTeX:
View
@article{SophiaChoandJohnC.Williams2026,
author={Sophia Cho and John C. Williams},
title={The R*–Labor Share Nexus},
journal={Liberty Street Economics},
note={Liberty Street Economics Blog},
number={April 15},
year={2026},
url={https://doi.org/10.59576/lse.20260415}
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Disclaimer
The views expressed in this post are those of the author(s) and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the author(s).
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