Exploring the R*–Labor Share Relationship and Its Economic Implications

In recent decades, the U.S. economy has witnessed notable trends: a decrease in both the labor share of income and the natural rate of interest, commonly referred to as R*. While prior studies have typically regarded these phenomena separately, this work introduces a unified model, termed the R*–labor share nexus, which suggests that changes impacting R* also influence the labor share. This relationship has direct implications for wages, prices, and macroeconomic policy considerations.

Examining Trends in Labor Share and R*

The falling trend in labor share and R* over the last 25 years is evident when reviewing data from the U.S. nonfarm business sector. Historically, from 1970 to 2000, the labor share, defined as the proportion of economic output allocated to workers for their labor, fluctuated between 60% and 65%. In stark contrast, more recent figures show this share has now dipped to approximately 55%.

Meanwhile, R*, reflecting the real interest rate whereby output meets its natural rate while maintaining stable inflation, has demonstrated a parallel decline. Estimates from the Holston–Laubach–Williams (HLW) model show R* fluctuated between 2.5% and 4% from 1970 until about 2000, before dropping to around 1% in the late 2010s. The concurrent movements of the labor share and R* raise intriguing questions about their interrelationship.

Understanding Correlation vs. Causation

Despite the noteworthy co-movement of the labor share and R*, it is crucial to interpret these patterns with caution. The similarity in trends may stem from random chance rather than a direct causal relationship. This common phenomenon observed in unrelated data series underscores that “correlation does not imply causation.” Thus, it's necessary to investigate underlying economic theories and statistical methodologies that may explain or confirm the observed correlations.

Theoretical Foundations

Economic theory provides critical insights into the R*–labor share linkage by exploring shared factors impacting both elements. Various studies have considered determinants affecting labor share, including technological advancements, changes in productivity and demographics, market power exercised by firms, globalization trends, and measurement complexities.

On the side of R*, research suggests a positive correlation between economic growth and R*, consistent with the permanent income hypothesis. In contrast, deviations such as life expectancy present a negative relationship with R* as explored in existing literature. Notably, these discussions highlight the potential for converging factors to influence both the labor share and R* jointly, hinting at an underlying connection that warrants empirical analysis.

For instance, a model proposed by Grossman et al. (2021) speculates that the labor share positively correlates with productivity growth while negatively associating with life expectancy, signifying a long-term relationship between these variables. Analyses related to R* support similar conclusions, reinforcing the premise that shifts in growth and life expectancy could alter both factors.

Empirical Analysis of Labor Share and R*

Given these theoretical insights, the next logical step involves examining the relationship empirically. Employing the natural logarithm of the nonfarm business labor share and the HLW estimates of R* as of 2025:Q4, we assess a long-run relationship through cointegration— a method applied to analyze nonstationary variables.

The findings reveal convincing evidence of cointegration between the labor share and R*, suggesting that these two time series can maintain a stable relationship over the long term. Subsequent testing of the relationship solely with the trend growth rate component of R* yields less definitive results. This indicates that additional factors influencing R*, beyond just trend growth, significantly contribute to the strong connection observed with labor share.

Modeling the Labor Share

In light of these results, we develop a straightforward model where the trend labor share (denoted S*) correlates directly with R* and a constant. The relationship can be articulated as S* = αR* + θ, where the labor share progressively adjusts toward this trend value over time. Notably, our baseline model estimates indicate that a 1 percentage point rise in R* translates to a 0.044 increase in the (log) trend labor share, amounting to roughly a 2.5 percentage point increase when averaged against a 60% labor share.

To further assess this dynamic, we consider the parameters over periods leading up to 2025, finding that approximately three quarters are required to close half of the gap between actual and trend labor share values. The goodness of fit in tracking actual labor share trends within our modeled forecasts affirms the robustness of the derived relationship.

Insights into Monetary Policy Impacts

The implications of these findings for monetary policy cannot be overstated. Given that much of the variation in labor share can be associated with shifts in R*, it suggests that structural changes impacting R*—such as variations in productivity growth, technological changes, or demographic shifts—possess broader ramifications for wages and prices than traditional macroeconomic models assume.

This relationship indicates a need for policymakers to consider the joint dynamics of R* and labor share when evaluating macroeconomic effects stemming from shifts in influential factors. Specifically, periods characterized by low R* are likely to coincide with diminished labor shares, while enhanced growth prospects could concurrently elevate both R* and labor share.

Conclusion and Future Directions

The R*–labor share nexus emphasizes the intricacies of the interconnections within the economy, urging economists and policymakers alike to reevaluate the potential impacts of structural changes on both fronts. An in-depth understanding of these evolving relationships can furnish more effective monetary policies that consider both wages and interest rates, thereby fostering healthier economic outcomes.