Over the previous quarter century, the U.S. economic system has skilled vital declines in each the labor share of earnings and the pure fee of curiosity, known as R*. Present 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 probably vital channel, absent from many macroeconomic fashions, via 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 under. The labor share is “the fraction of financial output that accrues to staff as compensation in change for his or her labor” (Giandrea and Sprague 2017). The blue line exhibits the labor share within the U.S. nonfarm enterprise sector, which fluctuated between 60 and 65 % from 1970 to 2000, then declined to about 55 % lately. An analogous sample is noticed throughout various measures of the labor share. R* is “the true rate of interest in keeping with output equaling its pure fee and secure inflation” (Laubach and Williams 2003). The crimson line exhibits 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 % from 1970 to 2000, then declined to about 1 % lately.
Parallel Motion of the Labor Share and R*
Be aware: This chart plots the labor share of earnings within the U.S. nonfarm enterprise sector and estimates of the U.S. pure fee of curiosity, R*, from the Holston–Laubach–Williams (HLW) mannequin, from 1970:Q1 to 2025:This fall.
A putting function of the above chart is the shut parallel motion of the labor share and R* over time. Nonetheless, this visible similarity needs to be interpreted with warning. Many unrelated information sequence exhibit related developments over stretches of time, so the discovering that two sequence look alike might merely replicate random probability. As well as, one ought to heed the adage that “correlation doesn’t suggest causation”: the labor share and R* will not be instantly linked, however quite collectively influenced by different components. To deal with these points, researchers flip to financial concept and statistical strategies to raised perceive the sources and nature of correlations over time.
Let Principle 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 expertise and productiveness, demographics, companies’ market energy in value 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 optimistic relationship between development and R* implied by the everlasting earnings speculation, whereas Carvalho et al. (2016), Mian et al. (2021), Auclert et al. (2025), and Carvalho et al. (2025) spotlight a unfavorable relationship between life expectancy and R*. Eggertsson et al. (2019) and Rachel (2025) analyze extra advanced fashions that enable for added influences on R*, together with modifications in expertise, market energy, international components, fiscal coverage, and the labor share. Bom et al. (2005) additionally hypothesize that R* will depend on the labor share.
Taken collectively, these two literatures counsel that frequent components might have an effect on the labor share and R* in the identical course, 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 development and negatively associated to life expectancy. This optimistic longer-run relationship between development and the labor share is supported by proof in Charpe et al. (2020). The literature on R* yields the identical qualitative predictions for the way development and life expectancy have an effect on R*. On the identical time, one shouldn’t count on the correlation between the labor share and R* to be actual, as every could also be affected by further idiosyncratic components. These concerns information the empirical evaluation that follows.
From Principle 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. Be aware that HLW estimates of R* include two parts: the estimated pattern development fee of the economic system and an unobserved variable that displays influences on R* past pattern development.
We start by testing for a longer-run relationship between the labor share and R* utilizing cointegration, a normal 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 robust proof of a cointegrating relationship between the labor share and R*, implying {that a} linear mixture of those two time sequence displays a secure and bounded longer-run relationship. Subsequent, we check for a longer-run relationship between the labor share and solely the pattern development part of R*, however we don’t discover equally robust proof. This implies that the opposite part of R*, which displays influences past pattern development, additionally performs an vital function in explaining the robust relationship between the labor share and R*.
Primarily based on this statistical evaluation, we posit a easy mannequin of the labor share, through which the pattern labor share will depend on R* and a relentless, and the precise labor share adjusts towards this pattern worth over time. Particularly, the pattern 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 pattern values.
The primary column of the desk under studies the mannequin’s parameter estimates for the pattern 1970–2025, which we consult with because the baseline specification. The estimate of α implies {that a} 1 share level enhance in R* is related to a 0.044 enhance within the (log) pattern labor share. Evaluated on the pattern common labor share of 60 %, this corresponds to roughly a 2½ share level enhance within the pattern labor share. The estimate of ρ implies that it takes about three quarters for half of the hole between the precise and pattern labor share to shut.
Labor Share Mannequin Parameter Estimates
| Pattern | |||||
| Parameter | 1970–2025 | 1970–2025 with time pattern |
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 studies parameter estimates from a number of specs of our labor share mannequin, through which the pattern 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 pattern values. The primary column studies estimates for the pattern 1970–2025 (baseline specification). The second column studies estimates for the pattern 1970–2025 together with a time pattern with parameter τ. The third via fifth columns report estimates for various samples 1970–2005, 1970–2015, and 1965–2025. Normal errors are in parentheses. The underside row studies the usual error of every regression.
The chart under exhibits that the mannequin’s dynamic forecast of the labor share (crimson line)—based mostly solely on R* and the mannequin’s parameter estimates—tracks the precise labor share (blue line) effectively, capturing each longer-run developments 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 based mostly 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, equivalent to together with a time pattern and utilizing various samples, offering additional assist that the connection between the labor share and R* just isn’t spurious. The second column of the above desk studies parameter estimates from a specification that features a time pattern within the pattern labor share. The estimated parameter on the time pattern, denoted τ, is statistically insignificant, and the estimate of α—which measures the power of the connection between R* and the pattern labor share—is barely modestly smaller than within the baseline specification. This means that the connection between the labor share and R* just isn’t merely the results of each having downward developments over the pattern. The third via fifth columns of the above desk report parameter estimates for various samples. The estimates of α are fairly related throughout samples, no matter whether or not they embody the interval of sharp decline within the labor share following the 2007–2009 recession.
Up thus far, by assuming that θ is fixed, we’ve successfully assumed that R* is the one issue influencing the pattern labor share. We now loosen up this assumption by permitting θ to range over time, capturing further influences on the pattern 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 exhibits 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 atmosphere that have an effect on R*—equivalent to shifts in productiveness development or demographics—might have broader implications for wages and costs than is usually assumed in macroeconomic fashions that deal with the labor share as fixed. Accordingly, one ought to take note of 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 pattern development fee of the economic system might increase 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 govt officer of the Federal Reserve Financial institution of New York.
The right way to cite this publish:
Sophia Cho and John C. Williams, “The R*–Labor Share Nexus,” Federal Reserve Financial institution of New York Liberty Avenue Economics, April 15, 2026, https://doi.org/10.59576/lse.20260415
BibTeX: View |
Disclaimer
The views expressed on this publish are these of the writer(s) and don’t essentially replicate the place of the Federal Reserve Financial institution of New York or the Federal Reserve System. Any errors or omissions are the accountability of the writer(s).
