Abstract
We calibrate an overlapping-generations model with a rich demographic structure to observed and projected changes in U.S. population, family composition, life expectancy, and labor market activity. The model indicates that demographic factors associated with the post-war baby boom pushed up real interest rates and real gross domestic product (GDP) growth from 1960 to the 1980s. Since the 1980s, the model accounts for a little more than a 1-percentage-point decline in both real GDP growth and real interest rates—much of the permanent declines in those variables according to some estimates. Our model predicts GDP growth and interest rates will remain low by historical standards, consistent with a “new normal” for the U.S. economy.
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Notes
The expression “secular stagnation” was popularized during the Great Depression by Hansen (1939), who wrote: “[this] is the essence of secular stagnation—sick recoveries which die in their infancy and depressions which feed on themselves and leave a hard and seemingly immovable core of unemployment.” One potential contributor to secular stagnation in the twenty-first century is a step down in technology growth, with authors such as Fernald (2015) and Gordon (2016) arguing that the high productivity gains enjoyed before the early 1970s and during the information technology boom of the mid-1990s to early 2000s are unlikely to be repeated.
For an early use of the expression “new normal,” see El-Erian (2010).
The baby-boom generation consists of the cohorts born after World War II through the mid-1960s; see Hogan et al. (2008) for a statistical definition.
See Bloom et al. (2009) for evidence that a fall in fertility rates causes a rise in female labor force participation.
For recent empirical evidence of the historically low correlation between real economic growth and real interest rates, see Bosworth (2014) and Hamilton et al. (2016). See also Lunsford and West (2019) for the evidence of the superior explanatory power of demographic variables compared to real economic growth over long horizons.
Consistent with this prediction, Browning and Ejrnæs (2009) provide evidence that two-adult households without children—for which household consumption roughly equals adult consumption—have fairly flat consumption profiles over their midlife.
One limitation of our approach is that extensions of the model that are not amenable to transforming the household equilibrium conditions into a set of linear equations conditional on aggregate variables would call for the use of nonlinear solution methods. One such extension is the inclusion of intentional bequest motives. Several authors have solved such problems by limiting the set of demographic (see, for example, De Nardi et al. (2016)).
We use annual estimates of live births from NCHS. The NCHS also makes available monthly data on live births; however these data contain apparent seasonal patterns.
To extract the trends in quarterly EPR series, we use the Hodrick–Prescott filter with a Lagrange multiplier of 25,000. This value is much higher than the typical value of 1,600 used in the business cycle literature. However, we found that the typical multiplier is much too low to filter out the cyclical effects of the Great Recession. See our technical appendix for further discussion.
These patterns are consistent with several and at times offsetting factors, including increased access to public and private savings and pension funds, improved health and access to health insurance, and longer life expectancy. For a recent overview of the literature on the labor supply of older workers, see Coile (2015).
The main productivity series published by Fernald (2014) excludes the contribution of aggregate labor quality growth, which we re-introduce for consistency with our model and the estimates of Shackleton (2013) and Gordon (2015). In Sect. 6, we show the robustness of our key findings to adding aggregate labor quality to our baseline calibration.
We again use the Hodrick–Prescott filter with a Lagrange multiplier of 25,000 on quarterly data.
Moreover, the 1900 Census counts by age are imprecise, displaying jumps in the number of persons reporting that their age in years ends with either a 0 or a 5. The quality of Census data appears to have improved quickly thereafter, making us confident that our key findings are insensitive to reasonable deviations from the initialization of demographic data. In any case, we smooth the 1900 Census counts when we initialize the age distribution.
For comparison with our model predictions, we report time-series estimates that are “two-sided,” that is, for each period, we report estimates that use all past and future information to infer the equilibrium real interest rate. The time-series studies sometimes emphasize one-sided and/or real-time estimates, which speak to when changes in equilibrium real rates became apparent in the data.
That is, we assume that a person aged a in any period after 1960:Q1 faces the same mortality rate, fertility rate, and employment rate (or combinations of these three variables, depending on the simulation) as someone aged a did in 1960:Q1 under our baseline calibration. The net migration flows by age and period are kept the same as under our baseline calibration.
That said, we view the typical value of the Hodrick–Prescott filter Lagrange multiplier for quarterly data, at 1,600, as much too low to eliminate all cyclical fluctuations, especially in light of the unusually prolonged recovery from the global financial crisis.
Cognizant of these limitations, Carvalho et al. (2016) write that “[the tractability of their age-independence assumptions] comes at the cost of not endowing the model with any flexibility to match the empirical age distribution. This additional feature would require an overlapping generation (OLG) model that is more computationally intensive and less analytically tractable. Hence, in our quantitative exercise, we can only target a few demographic statistics. We leave for future research an extensive comparison of the results obtained in this framework with those from a large-scale OLG model, disciplined by a richer set of moments from demographics data.” We see a contribution of our study as providing this important comparison point.
In addition to using a different modeling framework, these authors assume that the simulated economy begins from a steady state in 2005, whereas we compute a dynamic equilibrium over a much longer period.
See our appendix and replication materials for details on the construction of our series. Consistent with our earlier approach, we assume that these developments are anticipated and calibrate the household’s discount factor, \(\beta\), such that the average real rate in the 1980s corresponds to the average point estimate of Johannsen and Mertens (forthcoming). Absent this adjustment to the calibration, the introduction of positive technology growth in the model would raise the entire path of the equilibrium real rate compared with our baseline specification with no technology growth.
At business cycle frequencies, one might expect that calibrating the model to match data on the aggregate labor supply would mostly capture movements in aggregate output given that the capital stock is relatively fixed in the near term. However, at low frequencies, the endogenous dynamics of capital accumulation is also potentially important for explaining movements in the trend of real GDP growth.
The average the labor quality growth in the first and last 10 years of the sample in Fernald (2014) is similar to the sample-wide average, with some variation being observed over the in-between decades. Accordingly, we use the sample-wide average to impute labor quality growth in the simulation periods not covered by this author’s sample.
The evidence reviewed in Chirinko (2008) is consistent with a long-run elasticity somewhere between 0.4 and 0.6, with the preferred value of the more recent study by Chirinko and Mallick (2017) being at the bottom of that range. Under a standard CES production function, one cannot lower the elasticity parameter down to that range while simultaneously imposing that the share of capital in aggregate income is aligned with that in the data. In particular, for a capital share of aggregate income \(s_{K}\) and a balanced-growth real return on capital (net of depreciation) of r, Equation (4) requires setting \(\alpha\) equal to \(r^{\rho }/(s_{K})^{\rho -1}.\) If we were to set r such that it conforms with the estimates of Johannsen and Mertens (forthcoming) in the 1980s, then the value of \(\alpha\) consistent with \(s_{K}\)=0.35 would exceed 1 whenever the elasticity of substitution between capital and labor is assumed to be below 0.72.
We calibrate the discount rate such that the model with dependents matches the observed average level of interest rates in the 1980s. Without this normalization, the equilibrium real interest rate would be \(1\frac{1}{2}\) percentage points higher since the 1960s than otherwise. In that sense, the inclusion of dependent children in our model is consequential for our calibration and for the mix of factors that explain the overall level of interest rates.
See Section D of our appendix for a discussion of historical demographic projections for the United States.
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The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System. Declarations of interest: none. We are grateful to Sarah Baker, Carter Bryson, and Kathryn Holston for excellent research assistance, and to seminar participants at the Bank of Canada, the Danish Central Bank, Erasmus University in Rotterdam, the Federal Reserve Board, the 7th Joint Bank of Canada and European Central Bank Conference, the Centro de Estudios Monetarios y Financieros, the Einaudi Institute for Economics and Finance, the Federal Reserve Banks of Chicago, Kansas City, and Minneapolis, the International Monetary Fund, the Sveriges Riksbank, and the “Declining Natural Rate of Interest” session organized by the Washington Center for Equitable Growth at the 2018 annual meetings of the Allied Social Science Association. We further thank Linda Tesar and two anonymous referees for their input. Comments can be directed to benjamin.k.johannsen@frb.gov.
