The Effect of Population Aging on Economic Growth, the Labor Force and Productivity

Transcription

1 The Effect of Population Aging on Economic Growth, the Labor Force and Productivity icole Maestas Kathleen J. Mullen David Powell Harvard University and RAD RAD BER September 2018 Abstract Population aging is expected to slow economic growth yet there is little evidence about the magnitude of its effects. We use variation in the predetermined component of population aging across U.S. states to estimate the impact of population aging on GDP growth between We find that each 10% increase in the fraction of the population ages 60+ decreased percapita GDP by 5.5%. Two-thirds of the reduction was due to slower growth in productivity, while one-third arose from slower labor force growth. Our estimate implies population aging reduced the annual rate of GDP growth by 0.3 percentage points during JEL Codes: J11, J14, J23, J26, O47 Keywords: population aging, demographic change, GDP growth, economic growth, productivity growth We are grateful to the Alfred P. Sloan Foundation Working Longer Program for grant funding. We thank Axel Börsch-Supan, David Cutler, Mary Daly, Edward Glaeser, Claudia Goldin, Larry Katz, Jim Poterba, Dan Wilson, Robert Willis and the CBO Panel of Economic Advisers for valuable feedback, as well as participants of the 2014 SIEPR/Sloan Working Longer Conference at Stanford University, the Harvard Labor Economics Seminar, and CEPRA-BER Conference on Ageing and Health (Lugano) for their many helpful comments.

2 As the populations of developed countries become older than ever before, a persistent question has been what impact will this unprecedented demographic change have on economic growth and consumption standards? While several studies have sought to forecast the effect of population aging on economic growth (e.g., Cutler et al., 1990; Börsch-Supan, 2003; Vogel, Ludwig, and Börsch-Supan, 2013; ational Research Council, 2012; Sheiner, 2014), there are few empirical estimates of the realized effect of aging on economic growth. This is a significant gap in knowledge. While demographic change is relatively easy to forecast because of its predetermined nature, the ensuing economic adjustments by individuals, firms, and policymakers are not similarly deterministic. It is thus difficult to forecast the future path of economic growth without also accounting for the economic adjustments that may dampen or amplify the effects of demographic change. This paper presents the first empirical estimates of the realized effects of population aging on U.S. economic performance since Our analysis begins with the observation that population aging has been playing out over recent decades with varying degrees of intensity in different regions of the country. For example, between 1980 and 1990, there was fast growth (above 15%) in the older (ages 60 and older) population share in most Western states and in the Rust Belt, while at the same time 15 states, including California, Texas, ew York, and Florida, experienced reductions in the older population share. Between 1990 and 2000, the population grew younger in all but 12 small states, as the large Baby Boom birth cohort passed through prime age, causing the older population share to temporarily decline. Population aging resumed force between 2000 and 2010, exceeding 15% in 20 states, including the northern Pacific and Mountain states, and nearly all the South Atlantic states. Despite this wide variation across states and over time, it would not be informative to simply compare the economic outcomes of states that experienced fast population aging to states that experienced slow population aging. This is because economic growth in a state can affect its age structure by influencing age-specific migration and mortality. For example, a negative trade shock disproportionately affecting one state could induce both a slowdown in economic growth and differential migration of younger workers to other states, making it appear as if population aging leads to slower economic growth when the reverse is true. This potential reverse causality makes it unlikely that the observed association between economic growth and population aging at the state level represents the causal impact of population aging. 1

3 evertheless, some of the observed variation in population aging across states was in fact determined many years prior; this historical age structure shaped the relative sizes of age cohorts far into the future. Under certain conditions, this predetermined component can be used as an instrumental variable for the realized aging experienced by a state many years later, thus enabling estimation of the causal effect of population aging on economic growth. The key identifying assumption is that a state s past age structure affects its future economic outcomes only by affecting its subsequently realized age structure, and not through any other channel. To satisfy the exclusion restriction, the past age structure instrument must be sufficiently predetermined so that it is not itself a function of long-run trends predictive of future state economic growth. To satisfy this requirement, we take the initial age structure in each state alternatively measured 10, 20, 30, and 40 years prior to the outcome year and apply national cohort survival ratios to predict the older population share in each state in the baseline outcome year. We study decadal changes in growth and aging to account for the independent effects of prior age structure. As the lags used to predict future population aging grow more distant, it becomes less and less likely that the initial age structure could have been influenced by the same trends driving contemporaneous economic growth in a state. We estimate the effect of state population aging measured as the 10-year growth rate in the older population share on decadal growth in state GDP per capita, using each of the lagged instruments separately. As the lags grow more distant, the strength of the instrument attenuates, but even so, the 30-year lagged instrument has a first-stage F-statistic of 85. Importantly, our estimates are stable across the different lagged versions of our instrumental variable, indicating little influence of unobserved trends on the instrumental variables estimates once we condition on state and time fixed effects, even at shorter lags of the initial age structure. As we detail below, the estimates are also robust to many alternative specifications, including a dynamic model with lags of the dependent variable. We also find that this result is robust to conditioning on other age group shares (and separately identifying them using the historical age structure). Our preferred elasticity estimates imply that 10% growth in the fraction of the population ages 60 and older decreases GDP per capita by 5.5%. Given our focus on decadal growth, we interpret our estimates as evidence of the effect of population aging on medium-run economic growth. 2

4 To understand the channels through which population aging reduces economic growth, we use growth accounting and channel decomposition to decompose GDP per capita into its constituent parts GDP per worker (productivity) and the number of workers per capita (labor force participation). We then regress each component of GDP growth on (instrumented) growth in the older share to obtain a set of coefficients that sum to the coefficient on the older share from the regression for GDP per capita (-5.5%). The coefficients from this channel decomposition exercise imply that a 10% increase in the older population share results in a 3.7% decrease in output per worker and a 1.7% decrease in workers per capita (for a total effect on GDP per capita of -5.5%). Thus, two-thirds of the aging-induced reduction in GDP growth per capita arose from a reduction in aggregate productivity growth, while one-third was due to a reduction in labor force growth. This finding is notable for two reasons. First, while it was expected that population aging would reduce labor force growth, it was not expected that population aging would reduce aggregate productivity growth (ational Research Council, 2012). Second, as aggregate productivity has reached historical lows in recent years (see Fernald, 2016 for a discussion), our estimates imply population aging has played a significant, if unexpected, role in that process. We also probe which of the productivity channels are most affected by population aging human capital, physical capital, and/or technology. Since physical capital and technology are not measured at the state level by the U.S. government, our approach is to estimate the effect of population aging on growth in human capital per worker, and then compare the magnitude of that effect to the total effect of aging on aggregate productivity growth (-3.7%). Re-estimating our main specification with labor income per worker (earnings plus non-cash compensation) as the dependent variable, we find that a 10% increase in the older share reduces labor compensation per worker by 3.3%. This implies that 89 percent of the effect of population aging on aggregate productivity growth is attributable to slowing labor productivity (-3.3 points out of -3.7%), with the remainder, a statistically insignificant -0.4%, attributable to the combined channels of capital and technology. To corroborate this result, we use researcher-compiled data on the physical capital stock by state and find little effect of population aging on growth in physical capital. We further confirm that the reduction in labor compensation per worker is fully accounted for by a reduction in compensation per hour worked, and not by a reduction in intensive margin labor supply (i.e., hours worked per worker). This result provides further 3

5 evidence that changes in human capital were the primary source of the aging-induced slowdown in aggregate productivity. As a final step, we examine earnings growth by age group to assess how the decline in productivity growth manifests across the age distribution. Population aging results in a 5% reduction in earnings growth among men ages and a 3.2% reduction among same-aged women. But, surprisingly, population aging also results in reduced earnings growth for younger men and women. In other words, population aging slows earnings growth across the age distribution, reflecting declines in the average productivity of workers in all age groups. Importantly, these spillover effects to younger workers do not appear to be driven by selection on the extensive labor supply margin, as we find population aging does not affect the employment rate of younger workers. Our results imply that population aging has had an important impact on the economic growth of U.S. states. Before extrapolating to the nation as a whole, it is important to consider the generalizability of estimates from a state-based research design to the national setting. Statebased research designs have clear advantages over time-series designs, which are vulnerable to bias from confounding trends, and cross-national designs, which are vulnerable to bias from unobserved heterogeneity in national pension systems, labor market policies and cultural norms. Indeed, an advantage of using variation across economic units within the same country is that these effects are held constant (e.g., Barro and Sala-i-Martin, 1992). But these advantages are not without tradeoffs. State-based research designs do not capture indirect effects of population aging on the federal budget (e.g., rising Medicare expenditures) or effects of federal policy responses to aging that accrue uniformly across states (e.g., tax increases to fund Social Security benefits). That said, our estimates do incorporate downstream economic responses to population aging that may possibly vary across states such as shifts in industry composition but, importantly, not migration and industry shifts that arise from other factors, such as trade shocks or changes in tax incentives that encourage firm mobility and differential migration of older versus younger workers. We examine the empirical importance of some of these downstream responses when extrapolating our estimates to the national context. With these advantages and limitations in mind, our estimates imply that population aging has had a substantial impact on the annual rate of growth in the United States and may continue to affect growth in the future. ationally, the older share increased by 16.8% in the United States 4

6 between 1980 and Our elasticity then implies per capita GDP over that period was 9.2% lower than it would have been absent the effects of population aging. In terms of annual growth, population aging reduced the annual growth rate by 0.3 percentage points during , when the average rate of annual growth was 1.88%. In the present decade, population aging is responsible for an average annual loss of 1.2 percentage points in annual GDP growth, and could account for an average annual loss of 0.6 points between Our paper contributes an essential piece of evidence to the literature on the macroeconomic effects of changes in population age structures. 1 This literature has relied on cross-country research designs or model calibration, and has directed attention to the effects of workforce aging on growth in output per worker (productivity growth), as opposed to the more encompassing effects of population aging, which also include the effect of aging on labor force participation and growth in output per capita. Most relevant to our paper are two studies by Feyrer (2007, 2008). Using a panel of OECD and low-income countries between 1960 and 1990, 2 Feyrer found that the estimated relationship between worker age and total factor productivity was inverse-u shaped; that is, productivity growth increased with the proportion of workers ages but decreased as the proportion who were older rose. More recently, and contemporaneous with our study, the International Monetary Fund (Aiyar et al. 2016) used a cross-country design to estimate the impact of changes in the share of the labor force ages on output, instrumenting with the 10-year lagged value of the population share and conditioning on country fixed effects. They found evidence of large labor productivity declines as the workforce ages. In the U.S. context, a recent working paper calibrates an overlapping-generations model to study the role of changing demographics on the recent slowdown in growth (Gagnon et al., 2016). The model attributes the entire decline in real GDP growth since 1980 to population aging. Finally, while our paper addresses population aging as the large baby boom cohort exits the U.S. labor force, Shimer (2001) investigated the effect of the baby boom s entry into the U.S. 1 Other studies in the growth literature have considered the importance of the dependency ratio without focusing on population aging specifically. Bloom, Canning, and Sevilla (2003) examine the implications of a changing age structure for economic growth in developing countries. Kögel (2005) measures the effect of changes in the youth dependency ratio on total factor productivity. More recently, Aksoy et al. (2015) model the effects of demographic changes on long run economic growth accounting for endogenous fertility, education and innovation. 2 Feyrer (2008) also estimated models of changes in wage growth on changes in the age distribution of the workforce at the state and metropolitan levels using U.S. data; however, the estimates were not statistically significant. 5

7 labor force between Using state-level variation, he found that a 10 percent increase in the youth share (ages 16-24) increased the aggregate labor force participation rate by 2-3 percent. To address endogenous migration, Shimer (2001) used historical fertility rates, which parallels our use of the historical age structure in a state to predict differential aging. In the next section, we describe our data and summarize the variation in population aging and economic growth across states between 1980 and In Section II, we present our instrumental variables research design. Section III shows our estimates of the effect of population aging on economic growth, along with a series of robustness tests. In Section IV, we use a standard model of production to illustrate the potential channels through which population aging operates, and then we use channel decomposition techniques to estimate which channels are relatively more affected by population aging. We investigate effects by industry in Section V, followed by spillover effects on younger workers in Section VI, and effects on skill reallocation in Section VII. We conclude in Section VIII with a discussion of the implied magnitudes of our estimates for recent and future annual economic growth. I. Population Aging and Economic Growth: Data and Summary Statistics The U.S. population has aged nearly continuously over the last century. Figure 1 shows the percent of the population aged 60 and older between 1900 and 2000, and the projected percent through The only decade in which the population did not age was the 1990s when the baby boom passed through the middle of the age distribution. The U.S. population is projected to continue aging, at a relatively faster rate through 2030 (due again to the baby boom), and at a slower rate thereafter. U.S. population aging today results from the sharp decline in the birth rate in the 1960 s, which marked the end of the Baby Boom, and the long-running decline in mortality rates. Immigration can offset these demographic forces to some degree but has not been of sufficient magnitude to reverse population aging. To investigate population aging at the state level, we use state population counts by age from the 1950, 1960, 1970, 1980, 1990, and 2000 Census Integrated Public Use Microdata Series (IPUMS) and the American Community Surveys (ACS) (Ruggles et al., 2015). Due to the relatively small size of the ACS, we combine the samples to construct a

8 Census. 3 In addition to population counts, the Census and ACS contain individual-level data measuring employment status, hours worked and labor earnings in the preceding calendar year. 4 We aggregate these data to the state-year level to obtain the state employment rate, total hours worked and total labor earnings. To facilitate sub-analyses by sector, we construct a parallel set of population and labor market measures at the level of two-digit industry, state and year. 5 To measure aggregate economic output, we acquire GDP (in 2015 dollars) by state and year from the Bureau of Economic Analysis (BEA). 6 State GDP is defined as the value added in production by the labor and capital located in a state, measured in 2015 dollars. These data provide a comprehensive measure of a state s production (BEA, 2006). 7 The state GDP data also include industry-specific output measures, which we use to study the differential impacts of aging on different sectors of the economy. Because the annual labor outcomes from the Census and ACS refer to the previous year (i.e., 1979 in the 1980 Census), we match GDP data from the year preceding the indicated Census year (i.e., 1979, 1989, 1999 or 2009). 8 However, for ease of exposition, we refer to the Census years when indexing by time below. The BEA also collects state-level data on total employee compensation, which includes wages and salaries paid to employees as well as noncash benefits. Wages and salaries are the 3 Alternatively, we could have used state-level population statistics from the Census. However, we chose to construct our population size and labor supply measures from the same individual-level data in order to minimize differences arising from differences in data aggregation procedures. Using these noisier measures of state-level population should not affect the consistency of our estimates but may increase our standard errors. 4 There is evidence that the income data between the Census and ACS are not comparable due to survey changes. (last accessed August 18, 2018) finds that ACS household income is 4.6% lower than Census household income. We assume that time fixed effects account for this change or, more precisely, that this change is not correlated with our instrument after conditioning on time fixed effects. We also show results by decade. The and samples rely on Census data only and avoid this issue. 5 We use the 1990 Census Bureau industrial classification scheme, which is consistently reported in IPUMS for all years since Last accessed March 31, The BEA cautions that there is a discontinuity in the state GDP time series due to a switch from SIC industry codes to AICS industry codes. We assume that time fixed effects account for this shift and that any differential changes across states are not correlated with our instrument (predicted changes in aging). The literature has appended pre-1997 state GDP data to post-1997 state GDP data before (e.g., akamura and Steinsson, 2014). Also note that we present results by decade, which show that our results are not driven by changes between 1990 and An advantage of using aggregate production instead of consumption data is that GDP includes asset income, which can be used to compensate for declines in consumption. 8 There is still a slight misalignment between state and year for the labor outcomes since, before 2000, the Census only included information on state of residence in the current year. For 2000 and 2010 it is possible to aggregate labor outcomes by state of residence in the previous year. We conducted robustness checks of our main regressions for using the aligned and misaligned measures, respectively, and found that this did not affect our results. These estimates are shown in Appendix Table A.10 and discussed below. 7

9 primary component of employee compensation and include overtime pay, sick and vacation pay, severance pay, incentive payments (e.g., commissions, tips, and bonuses), and voluntary contributions to deferred compensation plans. oncash benefits include in-kind benefits and employer contributions to pension plans, health insurance, and social insurance programs. We use the BEA employee compensation data as a measure of full labor compensation in a state, and as a complement to the Census earnings data. 9 We construct growth rates by state for all of our analysis variables. These data are presented in Table A.1, where growth in a variable as of Census year t refers to the percent change between t-10 and t. The top panel shows all Census years pooled, while the lower panels show the data decade by decade. There is significant variation across states in the size and growth rate of the 60+ population in all years. In the pooled sample, the fraction ages 60+ ranges across states and Census years from to 0.313, with mean 0.24 and standard deviation The 10-year growth rate of the fraction 60+ ranges from -9% to 47%, with mean 4% and standard deviation 8%. Economic growth also varies substantially across states and years. In the pooled state-year sample, the 10-year real growth rate in GDP per capita ranges from -12% to 131%, with mean 55% (equivalent to annual state-level growth of about 4.5% 10 ) and standard deviation 26%. Productivity growth, measured as the 10-year growth rate in GDP per worker, ranges from -8% to 117%, with mean 55% and standard deviation 19%. Finally, labor force growth, the other component of growth in GDP per capita, ranges from -10% to 9%, with mean -0.3% and standard deviation 4%. The regional patterns underlying the variation in population aging in Table A.1 are shown decade by decade in Appendix Figures 1A, 1B, and 1C. 11 Between 1980 and 1990 (Appendix Figure 1A), there was relatively fast growth in the older population in the West and in the Rust Belt. At the same time, 15 states, including the large states of California, Texas, Florida, and ew York, experienced a contraction in the relative size of their older population. Between 1990 and 2000 (Appendix Figure 1B) the majority of states experienced declines in the relative 9 One limitation of the BEA measure of total compensation is that it does not include compensation for the selfemployed. Adding in labor earnings for the self-employed using the Census and ACS has little effect on the results. 10 There are two differences between this rate and national per capita GDP growth over this time period (which is smaller). First, we are scaling GDP by the size of the population ages 20+, not the full population size. Second, we are reporting the average growth rate across states weighted by population size. To construct the national growth rate, one would want to weight by GDP size in the initial period. 11 Hawaii and Alaska are not shown in Appendix Figures 1A-1C, but are included in our analysis sample. 8

10 size of their older populations, with just 12 small states seeing weakly positive growth. However, between 2000 and 2010 (Appendix Figure 1C) the growth rate of the older population was above 15% in 20 states, including the northern Pacific and Mountain states, and nearly all of the South Atlantic states. Only 4 states Florida, orth Dakota, South Dakota, and the District of Columbia experienced less than 5% growth during this period. Florida is notable in that by this time it already had a relatively high older population share. Appendix Figures 2A-2C show the equivalent variation in economic growth rates by state and decade. II. Research Design Our causal model of interest relates the older population share in a state to state output per capita. To normalize comparisons of growth across states with different older population shares, we follow the related literature (e.g., Shimer, 2001) by using a log specification and taking first-differences to arrive at our specification for growth in GDP per capita between Census years t and t+10: ln ( GDP s,t+10 ) = β [ ln ( A s,t+10 )] + X s,t+10 st δ t + γ t + ε s,t+10, (1) s,t+10 where the outcome is the change in the log of GDP per person aged 20 and older in state s between Census year t and Census year t+10 (or a related outcome), Ast is the number of individuals aged 60 and older in state s and year t, st represents the state population aged 20 and older in year t, and Xst contains a set of time-varying control variables whose influence is also allowed to vary over time. 12 The γ t term represents time fixed effects and ε st represents state output shocks. The coefficient β measures the effect of the older population share on GDP per capita. By estimating in first-differences, we account for fixed differences across states. Under this specification, β is interpretable as an elasticity. We include in X the initial (period t) two-digit industry composition of the state labor force (specifically, the log of the fraction of workers in each industry 13 ) to further account for initial conditions that may predispose states to particular growth paths. 14 We will also show that our results are not sensitive to the log-log specification functional form shown in equation (1). 12 Both the outcome and main explanatory variable are normalized by the size of the 20+ population in the stateyear, which makes interpretation straightforward. Throughout the paper, we refer to variables normalized by the size of the 20+ population as per capita variables. 13 Results are similar throughout the paper if we use levels. 14 In complementary work, we find that an area s initial industry structure predicts changes in labor outcomes (see Maestas, Mullen and Powell, 2013). 9

11 While equation (1) relates state population aging to changes in state economic outcomes, changes in the age structure of a state may depend in part on factors related to economic growth. For example, economic decline could induce prime-aged workers to migrate out of the state while older workers may be more likely to stay given the smaller lifetime return to moving. Consequently, we would observe that aging states have less favorable economic outcomes, though this relationship is not causal. 15 Similarly, differential industry growth and decline across states may affect mortality rates and these mortality effects may not be uniform across all age groups, directly altering the age composition of states depending on their economic conditions. To address these potential confounders, we estimate equation (1) using an instrumental variables strategy that exploits variation in the predetermined component of population aging across states over time. The key identifying assumption is that a state s past age structure affects future changes in economic outcomes only by affecting its subsequently realized age structure, and not through any other channel. 16 To satisfy this requirement, we take each state s initial age structure alternatively measured 0, 10, 20, and 30 years prior to the baseline Census year t and apply common cohort survival ratios (as experienced nationally, not by state) to predict the older share of population in each state 10, 20, 30 and 40 years into the future. The key assumption of the instruments is that the age structure in prior decades does not independently predict economic trends. As the lags grow more distant, it becomes less and less likely that the initial age structure could have been influenced by the same trends driving contemporaneous economic growth in a state. More precisely, we use the age structure in year t-x to predict changes in the log of the fraction of the state population aged 60+ between periods t and t+10, where x {0, 10, 20, 30} corresponds to lag lengths of {10, 20, 30, 40} from t+10. For example, x=10 implies that the period t-10 age structure is used to predict both the period t and period t+10 age structures. 17 We refer to this as a 20 year lag length. Our instruments are generated using: 15 There is some evidence that population aging itself may affect interstate migration; see Karahan and Rhee (2014). 16 Alternatively, one can imagine using historical birth rates to predict current age structures. We do not take this approach for two reasons. First, given the timing of our data, we would need birth rates back to the early 1900 s. These are not available for many states. Second, there are advantages to generating predicted age structures using the age distribution at a fixed point in time. This approach permits us to test the sensitivity of the results as we go further back in time to generate the instruments. Using birth rates would require using a long time series of years to generate variation, and the equivalent sensitivity exercise would be more difficult. We do not find that our results are driven by the timing of the age structure that we use so there is likely little gain in altering this approach. 17 When x=0, the predicted period t age structure is the actual period t age structure. The instrument is the predicted change in aging given this original age structure. 10

12 ln ( A s,t+10 ) = ln ( A s,t+10 ) ln ( A s,t ) (2) s,t+10 s,t+10 s,t where A s,t+10 = j 60 x 10 js,t x A s,t = js,t x j 60 x Total number of people age j in state s at time t x Total number of people age j in state s at time t x j+x+10,t+10 j,t x ational survival rate of cohort age j between t x and t+10 j+x,t j,t x ational survival rate of cohort age j between t x and t and s,t+10 = js,t x j+x+10,t+10 j 20 x 10, s,t = js,t x j+x,t j,t x j,t x j 20 x. To predict the state age structure in year t, we use national census survival rates, defined as the ratio of the national population age j+x in one Census to the cohort s population size in a previous Census (at age j). 18 We then multiply the number of individuals age j in the state in one Census by the age-specific national survival rate to predict the number of individuals age j+x in the state in a subsequent Census. For example, to predict the number of 60-year olds in Alabama in 2000, we multiply the number of 40-year olds in Alabama in 1980 by the national ratio of 60- year olds in 2000 to 40-year olds in This approach uses the initial state age composition interacted with national level cohort changes and has the advantage of disregarding variation resulting from differential state-level migration and mortality for identification. 19 The instrument is similar in spirit to the Bartik instrument (Bartik, 1991; Blanchard and Katz, 1992), which predicts local economic growth by interacting national industry-specific growth with initial local industry composition. In the spirit of recent discussions of Bartik-like instruments (e.g., Goldsmith-Pinkham et al., 2018), we note that the main source of variation used by the instrument is the variation across states in the relative sizes of 10-year birth cohorts in year t-x ote our census survival ratios incorporate international (as opposed to interstate) migration. 19 Other approaches, such as using survival tables, for predicting national-level changes in cohort sizes are also possible. Since these national-level changes are simply being used to weight differences in earlier state-level age structures, there is likely little gain (or loss) in slight alterations of the proposed approach. 20 While Goldsmith-Pinkham et al. (2018) recommends using the baselines shares (in this case, baseline age shares) as instruments in themselves, this approach is disputed. See Borusyak et al. (2018) and Tim Bartik s comment found here: 11

13 For example, the 10-year lag primarily uses variation across states 10 years prior to t+10 in the size of their populations aged 50-59, while the 20-year lag uses variation across states 20 years prior in the number of year olds, and the 30-year lag uses variation from 30 years prior in the number of year olds. States that had relatively more individuals of a given age cohort in the past are predicted to experience relatively large increases in the number of older individuals in the future. 21 The assumption of this variation is that prior age structure does not predict changes in economic growth between periods t and t+10, except through its relationship with changes in population aging during that time period. We specify our main estimating equation in differences to account for the independent effects of prior age structure (and other cross-state differences) on current economic outcomes, but our main analysis will further consider the possibility of confounding trends. ote that for the instruments based on 30-year and 40-year lags we cannot predict the size of youngest age groups 30 and 40 years later since the youngest cohorts had not yet been born. We set the size of these cohorts to zero such that identification is originating from differential baselines for observed cohorts that predict the size of the 60+ age group, relative to observed cohorts that predict the size of the under-60 age group. Since no identification is originating from the assignment of these zeroes, this method should not create any problems, unless birth rates change systematically in our sample such that they unravel the first stage (i.e., substantially higher birth rates in areas that otherwise would have experienced growth in the elderly share). However, the existence of a strong first stage relationship would suggest this is not the case. Alternative imputation methods to improve the strength of these instruments are possible, such as predicting birth cohort sizes based on baseline demographics. However, the validity of the instruments would depend on the appropriateness of the underlying assumptions since some variation would originate from the imputation. Our decision is conservative and avoids identifying off of such assumptions. The variation in the population age structure that we exploit is predictable and observable by residents of the state before time t. In this manner, the instrument parallels population aging instrument (last accessed August 20, 2018). To summarize this emerging literature, there are benefits to providing weights to appropriately aggregate the initial shares into a single instrument, as we have done. 21 Some variation may also come from changes in the denominator. That is, if the younger population is (predictably) growing faster in one state than in another, the first state will have less population aging by our metric even if the two states experienced the same (absolute or proportional) change in the number of older individuals. 12

14 at the national level. The literature has used lags of the age structure to predict the current age structure as a way to avoid confounding by endogenous migration (Shimer, 2001; Jaimovich and Siu, 2009; Aiyar et al., 2016). We estimate equation (1) using 2SLS. We weight our regressions by period t population, though we provide unweighted estimates as well. We adjust standard errors for clustering at the state-level. 22 III. Effect of Population Aging on Economic Growth A. Main Estimates We begin with a visual depiction of our research design in Figure 2. Each data point is an observation of the decadal change in a state, weighted by population size in the base year. Figure 2A shows the strong negative association in the raw data between realized population aging and per capita GDP growth over the period Figure 2B shows the first-stage relationship between realized aging and predicted aging (using the 10-year lagged instrument). Here, we see that realized population aging is strongly predicted by the instrument. Finally, Figure 2C presents the visual reduced form relationship between the predicted aging instrument and subsequent economic growth, which is negative and statistically significant. Table A.2 presents the ordinary least squares (OLS) coefficients summarizing the relationship between aging and economic growth once we include controls for state industry composition in the base year and time fixed effects. The table shows OLS estimates of β (equation 1) for the entire time period , and separately for each decade. The dependent variable is the decadal change in log per-capita GDP in a state. The point estimates indicate that states experiencing growth in the fraction of individuals ages 60+ also experience slower growth in per capita GDP. Pooling all three decades, we estimate that a 10% increase in the fraction of the state population ages 60+ is associated with a decrease in per capita GDP of 8.3%. Contrasting this estimate with the much larger slope coefficient in Figure 2A reveals the importance of controlling for year fixed effects and baseline industry composition. Limiting the sample to one ten-year difference at a time, we consistently find a large and statistically significant conditional association between population aging and per-capita GDP growth. 22 We also apply a small sample adjustment for inference. 13

15 As noted above, there are many reasons why state populations might age at different rates and economic growth itself could impact the state age structure by affecting migration decisions; this would bias the OLS estimate away from zero if younger workers move to faster growing places to pursue new job opportunities or, conversely, if older individuals move to slower growing places to take advantage of the lower cost of living. Similarly, if economic growth affects mortality rates, then this too may contribute bias, though the direction of the bias is less obvious in this case since it depends on how any growth-induced mortality changes play out across the age distribution. Panel A of Table 1 presents the reduced form relationship between our instruments the predicted change in the log of the fraction of individuals 60+ in a state and economic growth. When we predict the older share using the age structure 10 years prior, we find that a 10% increase in the predicted older share results in a 3.9% decrease in per-capita GDP. Using the age structure 20 and 30 years prior to predict the older share results in nearly identical reduced form estimates of 3.1%. The reduced form using the age structure 40 years prior is somewhat smaller at 2.5%. Table 1, Panel B shows the first-stage coefficients for the different instruments, conditioning on year fixed effects and initial industry composition. When we predict the older share using the age structure 10 years prior, we find that a 10% increase in the predicted older share results in a 7.2% increase in the actual older share (compared to the unadjusted estimate of 8.3% in Figure 2B). As one would expect, the first stage generally decreases as we use longer lags of the age structure to predict future demographic changes: a 10% increase in the older share predicted from the age structure 20 years prior results in a realized 6.2% increase in the older share; the realized increase is 6.9% when we use the age structure 30 years prior and 4.6% when we use the age structure 40 years prior to predict the older share. Accordingly, the first-stage F- statistic is when we use a 10-year lag, for the 20-year lag, 85.1 with the 30-year lag, and 13.0 using a 40-year lag. The IV estimates of β are shown in Panel C Table 1. Across the board, the IV estimates are smaller in magnitude than the OLS estimate, consistent with bias in the OLS estimate from 14

16 economically-induced migration of younger individuals to faster growing areas. 23 Instrumenting with the 10-year lagged age structure, we estimate that a 10% increase in the fraction of the population 60+ decreases per-capita GDP by 5.5%. The estimates are similar when we instrument with longer lags of the age structure we obtain an estimated decrease of 5.0% using the 20-year lagged age structure, a 4.5% decrease with the 30-year lagged age structure, and a (statistically insignificant) 5.4% decrease with the 40-year lagged age structure. The consistency of the estimates across the instruments suggests that the IV estimate based on the 10-year lagged age structure is not confounded by underlying economic trends (i.e., that estimating in firstdifferences is appropriately accounting for the independent effects of the initial period-t age structure). We therefore use this more precisely estimated coefficient as our main estimate for the robustness tests and decompositions in the following sections. Appendix Table A.3 shows the reduced form, first stage, and IV estimates separately by decade. We estimate that aging reduces per-capita GDP in each decade. B. Robustness of the Main Estimates In this section, we examine the robustness of the main estimates to factors such as changes in the shares of younger age groups, confounding trends in output or mean reversion, alternative functional forms, weighting, common regional shocks, and mis-measurement of state of residence. B.1. Robustness to Changes in the Share of Younger Age Groups While our specification models changes in per capita GDP as a function of changes in the older population share, economic growth may also be affected by changes at other points of the age distribution. Moreover, predicted increases in the 60+ population share may be correlated with predictable growth in the share of other age groups, suggesting the possibility of an omitted variable related to changes in other (correlated) age group shares. We can test for this possibility explicitly given that our instrumental variables strategy is easily extended to predict growth in other age groups. To implement this, we include multiple age groups in our specification and, as 23 The difference between the OLS and IV estimates using the 10 year lagged instrument is marginally statistically significant (p=0.06). We test the equality of the estimates through a clustered bootstrap method and report how frequently the OLS estimate is smaller than the IV estimate. 15

17 before, estimate our main model using two-stage least squares, where the instruments are the predicted changes in each included age group using the same prediction method as before (based on 10-year lags of the state age structure). The results are presented in Appendix Table A.4. We find that only growth in the 60+ population leads to a statistically significant decrease in GDP per capita. When we include all other age groups, our estimate is nearly the same as before a 10% increase in the fraction of the population aged 60+ is associated with a 5.9% decrease in per-capita GDP. Including or excluding the other age groups has little effect on this estimate. Consequently, we conclude that separately identifying these other age groups is unnecessary for consistent estimation in our context. We provide further support for this conclusion when discussing the role of functional form restrictions below and specifying age group changes in levels instead of logs. B.2. Robustness to Confounding Trends in Output or Mean Reversion Growth in a state s older share may be a function of the state economic conditions, potentially confounding the causal relationship between aging and growth. OLS estimates of equation (1), as shown in Table A.2, reveal a strong negative correlation between aging and growth, even when accounting for state fixed effects (through differencing) and time fixed effects. Our instrumental variable strategy is designed to disentangle the reverse effect of growth on realized population aging from the effect of population aging on growth by using predicted changes in the state s population structure. Our IV estimates suggest that the OLS estimates are, in fact, biased away from zero, as one would expect if the older share were systematically affected by economically-induced migration patterns. The instrumental variables strategy assumes that the initial age distribution of a state is not predictive of trends or mean reversion in economic output except through changes in the state age structure. Our main evidence that the identifying assumption is valid is the robustness of our estimates to use of longer lags of the age structure (Table 1). Further evidence supporting this assumption is that, if the initial age structure predicts differential economic growth, then we might expect to see statistical relationships across other age groups as well. However, as discussed above, Table A.4 (and also Table A.6, discussed below) shows that only changes in the share aged 60+ are statistically related to changes in per capita GDP. It is unlikely that the instrument for the change in the share 60+ (here, variation is primarily driven by differences in 16

18 the share ages years prior) would alone predict confounding trends, while variation in every other initial age group share would not (e.g., the instrument for the change in the share is here primarily based on the share years prior). Our final piece of evidence in support of the identifying assumption is presented in Appendix Table A.5, where we report estimates from a specification that controls for the initial (period t) log of per capita GDP in state s to account for trends dependent on initial economic conditions. This control is potentially important given previous evidence of convergence across states (Barro and Sala-i-Martin, 1992). Because of the biases associated with estimating a specification with a lagged dependent variable, we use the GMM estimator introduced in Arellano and Bond (1991). In Column (1), we present estimates using (all available) lagged values of the log of per capita GDP as instruments. The estimate is larger in magnitude than our main estimate. In Column (2), we replicate this specification but do not use the t-10 value of the log of per capita GDP as an instrument, relying only on lags further back in time. The exclusion of this instrument reduces the possibility that the lagged instruments are themselves endogenous due to serial correlation in the error term. The Column (2) estimate is even larger in magnitude. Overall, these results indicate that underlying trends and mean reversion are not driving our results. B.3. Robustness to Alternative Functional Form Assumptions Our main specification uses changes in the log of the older population share, given precedents in the literature. To test whether this log specification is driving our results, in Appendix Table A.6 we replicate Appendix Table A.4 using levels instead of logs and instrumenting with the corresponding predicted level changes. As before, the point estimates on the change in the older share are similar regardless of whether other age groups are also included in the model. We estimate that each percentage point increase in the older share decreases per capita GDP by 2%. Given that the mean older population share in the sample is 0.24, a 10% increase in the older share implies a reduction in per capita GDP of 4.9% (using the estimate in the final column), which is similar to our main estimate. ext, we estimate our model using Poisson regression. Santos Silva and Tenreyo (2006) show that a logged dependent variable in a linear regression restricts the error term. The specification in equation (1) assumes that the error term is multiplicative in per capita GDP 17

19 growth. Using an exponential specification and estimating with Poisson regression relaxes this assumption, allowing for both multiplicative and additive error terms (also see Santos Silva and Tenreyo (2006) for advantages of Poisson over related estimators such a negative binomial regression). We replicate our main analysis using instrumental variables Poisson regression and present the results in Appendix Table A.7. We find similar results as before, further suggesting that our estimates are not driven by functional form assumptions. B.4. Robustness to Weighting Appendix Table A.8 shows that the IV estimates are similar with and without weighting by state population size in the base year. Without weighting, we estimate a statistically significant effect of 4.8% in the pooled sample, compared to our main estimate of 5.5% with weighting. The point estimates for each decade estimated separately are negative, regardless of weighting. While we predict especially fast population aging in some states (e.g., Alaska), the inclusion or exclusion of these outlier states has little effect since they tend to be small. In related analyses, we have also estimated our main specification while dropping one state at a time. The elasticity estimates from this exercise vary between and and are always statistically significant from zero at the 5% level. Thus, our results are not driven by one particular state or outlier. B.5. Robustness to Common Regional Shocks, Mismeasurement of State of Residence In Appendix Table A.9 we show that our main estimates are robust to the inclusion of region-year interaction terms, and therefore common regional shocks are not driving our results. Appendix Table A.10 shows that the one-year misalignment in when residence is measured in the Census compared to state of residence in the previous year does not materially affect our estimates for the period (the one period in which both the current and prior year s state of residence are available). The IV estimate increases in magnitude when we use the prior year s state of residence. IV. Decomposing the Main Effect Labor Force and Productivity Growth Our main estimate implies population aging slows economic growth to a significant degree, but says little about mechanisms. Does population aging affect output by slowing labor 18

20 force growth or aggregate productivity growth? How much of the effect operates through changes in human capital, as opposed to physical capital or technology? In this section, we use growth accounting and channel decomposition to provide evidence on the relative importance of these different channels. We begin with a representation of state economic output in year t, using the Cobb- Douglas form with human capital (Mankiw et al., 1992; Feyrer 2007): Y st = K γ st H δ st (Ω st L st ) 1 γ δ, where Y is state output or GDP, K is the stock of physical capital, H is the stock of human capital, Ω is technology, and L is the state labor force. Following Wong (2007) and Feyrer (2007), we divide both sides of the production function by the labor force L st, 24 and let the lowercase letters y, k, and h denote the per-worker values of output, physical capital, and human capital, respectively. By taking logs and differencing the production function, we obtain an expression for growth in output-per-worker: ln(y st ) = γ ln(k st ) + δ ln(h st ) + (1 γ δ) ln(ω st ). (3) Using the decomposition and notation in Wong (2007), this expression shows that growth in output per worker (GOUTPUT), which we define as productivity growth, can be decomposed into physical capital accumulation (GCAPITAL), human capital accumulation (GHUMA), and technology growth (GTECH): GOUTPUT GCAPITAL+GHUMA+GTECH. (4) Our model in equation (1) explains per capita output, and we note that Y = Y L L, implying the decomposition: GOUTPUTCAP GOUTPUT+GLFP where GOUTPUTCAP designates per capita output growth and GLFP is labor force growth. It follows that the causal effect of population aging on growth in output (β) is the sum of its effects on physical capital accumulation, changes in the human capital composition of workers in the state labor force, technology growth, and changes in the state labor force participation rate: β β GCAPITAL + β GHUMA +β GTECH + β GLFP. (5) If we estimate equation (1) separately for each component of output growth (using the same IV approach as above), the component coefficients mechanically sum to β, the coefficient measuring the total effect of population aging on output growth. 24 As before, we define the number of workers as the number of workers ages

21 In practice, some components of output are not observed, but we can estimate equation (1) for the observed components and infer the relative importance of the unobserved components using the identity in equation (5). For instance, if we regress GLFP and GOUTPUT on population aging, we obtain estimates of β GLFP (the effect of population aging on labor force growth) and β GOUTPUT (the effect of population aging on aggregate productivity growth), which sum to β (the effect of population aging on output-per-capita growth). We show this first decomposition in Table 2. Here, we are defining productivity as GDP per worker before decomposing this term further. Column (1) reproduces the total effect of population aging on growth in GDP per capita (as presented in Table 1 Panel C), with each panel showing the estimates using the different lagged instruments. Columns (2) and (3) present the effects of population aging on aggregate productivity and labor force growth, respectively. As expected, population aging decreases labor force growth. Specifically, a 10% increase in the fraction of the population 60+ leads to a 1.7% decrease in workers per capita using the 10-yearlagged instrument. The estimate is slightly larger (1.9%) when we instrument with the 20-year lag, and slightly smaller (1.5%) with the 30-year lag. More surprisingly, population aging has a larger effect on aggregate productivity (Column 2): a 10% increase in the fraction of the population 60+ leads to a 3.7% decrease in GDP per worker using the 10-year lagged instrument, a 3.1% decrease instrumenting with the 20-year lag, and 3.0% decrease with the 30-year lag (the latter not statistically significant). By construction, the estimated effects of population aging on growth in GDP per worker (Column 2) and growth in workers per capita (Column 3) sum to the total effect in Column (1). 25 For each version of the instrument, the productivity estimate is larger in magnitude than the labor force estimate. Using the 10-year lagged instrument, the decomposition implies that approximately two-thirds of the effect of population aging on economic growth is because population aging slows productivity growth. To investigate this further, we first test whether the productivity effect is simply the result of changes in intensive margin labor supply given that we define productivity as output per worker. If, for instance, older individuals have a stronger preference for part-time work than younger individuals, then population aging should have less 25 Similar to our prior sensitivity test, we check whether these results are driven by not including other age groups in the specification. In Appendix Table A.11, we replicate Appendix Table A.4 using growth in the log of GDP per worker as the outcome variable. The effect of the older share is similar regardless of whether other age groups are included in the model. We obtain similar results when using age share levels instead of logs. 20

22 effect on output-per-hour worked, and a large effect on hours worked per person. To test this, we decompose aggregate productivity into two components, output per labor hour and hours worked per worker: Y/L = Y/HOURS HOURS/L, where HOURS is total state labor hours. We then estimate the effect of population aging on the difference in the log of each component, using the 10-year lagged instrument. The results are shown in Table 3. The estimate in the top row of column (1) indicates that growth in the older population share has little effect on the number of hours worked per worker (intensive margin labor supply). Rather, Column (2) shows that a 10% increase in the older share reduces GDP per hour worked by 3.4%. Because the intensive margin effect is small, the effect of population aging on growth in GDP per hour worked (Table 3, Column 2) is nearly the same as the effect of population aging on growth in GDP per worker (Table 2, Column 2). Thus the estimated productivity effect is not explained by reductions in the average number of hours worked. We next investigate which of the productivity channels are affected most by population aging physical capital, technology or human capital. Since these components of aggregate productivity are only partially observed, this decomposition is more challenging than the previous decompositions. oting that earnings are a measure of human capital (H), we further decompose output per labor hour into GDP per dollar earned by labor and earnings per hour worked (i.e., average wage): Y/HOURS = Y/E E/HOURS, where E represents labor earnings. As before, we estimate the effect of population aging on growth in the log of each component. If the effect of population aging on productivity growth reflects changes in the marginal product of labor, then earnings should adjust in response to changes in productivity. If such adjustments are occurring, then the decline in productivity growth should be reflected in the average wage 26 and the effect of population aging on growth in GDP per dollar earned should be zero. Our findings in Columns (3) and (4) of Table 3 support these hypotheses. A 10% increase in the fraction of the population 60+ decreases the average wage by a marginally statistically significant (p<0.10) 2.0% (Column 4), and decreases GDP per dollar earned by a statistically insignificant 1.4% (Column 3). The estimates in Columns (3) and (4) sum to the estimate in Column (2) by construction. Since labor earnings do not fully reflect labor costs due to benefits, we repeat the decomposition substituting BEA s measure of total labor compensation for labor earnings, 26 We use total earnings divided by total hours worked in a state, which is equivalent to a weighted (by hours) average of individual hourly wages. 21

23 presented in the bottom row of Table 3. In these models, we find an even stronger negative effect of population aging on growth in the average wage when it includes monetary and in-kind benefits. Our estimates imply that a 10% increase in the fraction of the population 60+ leads to a statistically significant (p<0.01) 3.3% decrease in average compensation per hour worked and a statistically insignificant 0.1% decrease in GDP per dollar of labor compensation. This analysis further indicates that changes in the aggregate human capital stock are the primary driver of the decline in productivity growth. The coefficients in Column 4 are also estimates of β GHUMA, the effect of population aging on changes in human capital. Because β GOUTPUT β GCAPITAL + β GHUMA +β GTECH, subtracting β GHUMA from β GOUTPUT gives an estimate of how much of the effect of aging on productivity growth operates through the channels of physical capital and technology. This exercise suggests that capital and technology together account for at most points (47%) of the productivity reduction if we do not count benefits as compensation, and just points (11%) when we include the value of benefits in total compensation. To add support for this conclusion, we use researcher-compiled data on the physical capital stock by state (government statistics on physical capital do not exist for U.S. states). Garofalo and Yamarik (2002) estimates state-by-state capital stock data to analyze convergence across states. These data were updated by Yamarik (2013) and used often in the literature studying cross-state capital stock variation (e.g., Peri, 2012; Reed, 2008; Han and Lee, 2016). These data do not extend to 2010 so we study for these analyses. 27 Using the same approach as above, we regress growth in the log of capital per worker (from and ), instrumenting for the older population share as before. Appendix Table A.12 presents these estimates. We obtain an estimate of β GCAPITAL equal to indicating that population aging had little effect on capital accumulation during that time period. While not statistically significant (and small in magnitude compared to the overall estimated effect of aging), the positive relationship between aging and capital is consistent with recent findings that population aging is associated with greater adoption of robots and other automation technologies (proxied by an indicator for whether a commuting zone houses robot integrators) (Acemoglu and Restrepo, 2018). 27 Data are found here: (accessed ovember 15, 2017) 22

24 Since there is no data measuring technology accumulation by state, we cannot perform the same validation exercise for technology. onetheless, if β GCAPITAL 0, then our estimates suggest that population aging has also had a relatively modest effect on technological growth. In conclusion, our decomposition exercises suggest that about 1/3 of the total effect of population aging on economic growth operates through changes in labor force participation. The other 2/3 of the total effect is due to changes in GDP per hour worked. We show that this reduction in productivity growth is matched by a reduction in wage growth, which points to the existence of labor market adjustments that compensate for real losses in the marginal product of labor and thus corroborates our finding that changes in human capital were the primary source of the estimated slowdown in productivity. In the next sections, we investigate whether the effect of population aging on output and productivity growth were concentrated in any particular industry or set of industries, and whether there were spillover effects from older to younger workers. V. Effects by Industry It is possible that population aging affects different industries to varying degrees, depending on the age structure of their workforce, industry-specific skill demands or whether the industry produces tradable or nontradable goods or services. Venn (2008) argues that the impact of aggregate population aging should vary across industrial sector due to productivity differences. In addition, shifting consumption patterns with age may induce changes in demand for particular kinds of goods and services. For example, as people withdraw from the labor force they tend to reduce consumption of work-related goods and services and increase consumption of healthcare services (Hurd and Rohwedder, 2008; Hurst, 2008). Our state-based research design will capture these aging-induced product demand shifts to the degree that goods and services demanded by older individuals are mostly consumed in the state where they are produced. An example of such a service is health care, which in most instances must be consumed where it is produced. 28 To explore this, we estimate equation (1) separately by industry. The dependent variable is based on industry-specific GDP per person in a state, and population aging is measured at the state level as before. We present these industry estimates in Appendix Table A.13. The first 28 As noted elsewhere, our research design does not capture changes in demand that drive production in other states (e.g., Internet sales) or that are dispersed uniformly across the national economy. 23

25 entry shows the effect of population aging on growth in output per capita of all private industries. This estimate is similar to our main estimate for total output per capita (private plus public sector) in Column 1 of Table 2, and implies our main estimate is not driven by changes in public sector output. The rest of the entries in Table A.13 show the estimated effects of population aging industry by industry. The largest effect arises in Construction. We estimate that a 10% increase in the fraction of the population 60+ decreases Construction output by 8.6%. We also find statistically significant aging-induced reductions in output in Wholesale Trade, Retail Trade, Finance/Insurance, and Services. The estimate for Manufacturing is of similar magnitude, but imprecisely estimated. These patterns suggest that the decrease in overall economic growth cannot be explained by a reduction in the growth of one or a small number of industries. Instead, it appears that population aging diminishes growth in most industries, although the estimates are statistically inconclusive for Agriculture, Mining, 29 and Transportation/Utilities. VI. Spillover Effects on Younger Age Groups Workers in different age groups may be substitutes or complements to one another and therefore the productivity of one age group can depend on interactions with workers in other age groups. Such productivity spillovers could occur between older and younger workers if, for example, an older worker s greater experience increases not only his own productivity but also the productivity of those who work with him. In this section, we examine the effects of population aging on the employment and earnings growth of men and women in different age groups to investigate the role of spillover effects from older to younger workers. First, we estimate equation (1) separately for men and women by ten-year age groups, where the dependent variable in each regression is the change in the log employment rate of the age-gender group. The corresponding estimates combining men and women are included in Appendix Table A.14. As before, the key independent variable in all models is the change in the log fraction of population ages 60+ (both genders combined), for which we instrument as above. The two-stage least squares estimates are shown in Table 4. We find little effect of population aging on employment growth in younger age groups, but larger reductions in employment growth in older age groups. The results suggest that an increase in the fraction of the population 29 The Mining sector workforce is expected to age rapidly over the next several decades (Brandon, 2012), but because of its geographic concentration within just a few states, we lack statistical power to detect effects on economic growth. 24

26 ages 60+ does not crowd out younger workers. Rather, the slowdown in employment growth induced by population aging was indeed concentrated among older individuals and, in particular, among older men. It is true, however, that as the population ages the workforce becomes older. Appendix Table A.15 shows how population aging induces an increase in the share of the workforce that is 50 and older and a decrease in the share under Table 5 presents the corresponding wage effects by age group and gender. 31 The wage estimates aggregating men and women are included in Appendix Table A.16. The outcome variable is the change in the log wage, which as before is defined as total labor earnings divided by total hours worked (by age group, gender, state, and year). Here, we find large effects of population aging on productivity growth among younger workers, as well as older workers. Our point estimates imply that a 10% increase in the fraction of population ages 60+ reduces productivity across the age distribution (through age 69), and for males and females alike, by 3-5%. Our estimates reveal how population aging-induced changes in labor supply alter the productivity composition of the workforce. We find that population aging leads to slower average wage growth for workers ages 60-69, which implies that individuals in this age range who retire tend to be more productive on average than those who stay in the workforce, that growth in the number of older workers drives down wages for the older age group, or both. The reduction in wage growth for younger workers could arise from the loss of positive production spillovers from retiring older workers to their younger counterparts if the productive older workers are more likely to retire. 32 More generally, lower average productivity among older workers may affect younger groups if younger and older workers are complementary inputs in production, resulting in slower wage growth for both groups. The relative productivity of older workers relative to younger workers may depend on work experience, health, education, and a host of other factors. Disney (1996) suggested the possibility that an older workforce is a more experienced labor force with the potential for improvements in productivity. To this point, Feyrer (2008) notes that typical estimates of the 30 ote our results illustrate that an aging-induced reduction in the younger employment share does not necessarily imply an aging-induced reduction in the younger employment rate. 31 In this analysis, we cannot account for the full compensation costs since the BEA does not estimate compensation data by age group. 32 ote the presence of negative wage growth effects across the age distribution is also consistent with efficiency losses arising from the thinning of labor markets in areas with faster population aging (Gan and Li, 2004). 25

27 return to experience from Mincer wage regressions imply a 60 percent difference between the productivity of 50-year old and 20-year old workers. A case study of German car manufacturers found suggestive evidence that more experienced older workers were more productive than younger workers (Börsch-Supan et al., 2008). More recently, Börsch-Supan and Weiss (2016) find no evidence of productivity declines up to age 60 at a large truck assembly plant. Until recently, this experience-productivity advantage was in part offset by the higher educational attainment of younger workers compared to older workers. But as a result of the secular growth in educational attainment through the 1970 s (Goldin and Katz, 2007), completed education among 65-year-olds is rising dramatically, from 10.1 years in 1980 to an expected 13.3 years in The subsequent slowdown in educational attainment means that, in sharp contrast, completed education among 25-year-olds is rising very little, from 13.3 years in 1980 to a projected 13.9 years in The net result is that the average older worker is now nearly as educated as the average younger worker. Age-related health differences may also offset part of the experience-productivity advantage, owing to the higher prevalence of disability with age. However, trends in health suggest this too may be lessening as obesity-related disabilities disproportionately affect younger cohorts (Freedman et al., 2013). Perhaps the biggest open question pertains to the age profile of cognition and its effect on work productivity. While some aspects of cognition decline gradually over the adult lifespan (e.g., processing speed), others hold steady until late life (e.g., knowledge) (Verhaegen and Salthouse, 1997), and there is considerable heterogeneity in the timing of decline across individuals (Hartshorne and Germine, 2015). Most intriguingly, cohort improvements in cognitive functioning point to a process of cognitive aging that is itself highly plastic (Staudinger, 2015). These age and cohort patterns in human capital acquisition and decumulation point to the possibility of heterogeneity in the effects of population aging on economic growth over time. Appendix Tables A.17-A.19 present the employment and wage effects by age and gender for each decade between 1980 and We find that the negative spillover effects on wages of younger workers were strongest in the 1980s when employment rates among older men were at their lowest point ever, when the human capital gap between older and younger workers was closing rapidly, and prior to the proliferation of desktop computers and the Internet. 33 Since then, 33 We do find some weak evidence of crowd out in employment of younger workers in the 1980s. 26

28 employment rates among older men and women have risen, and the diffusion of technology has changed the skill demands of many jobs. While further research is needed to identify the precise mechanisms at work, our findings foretell a further slowdown in productivity growth reflecting not only compositional differences in the workforce but also real productivity losses among individuals across the age spectrum. At the same time, greater investment in human capital development throughout the lifecycle, greater utilization of labor-augmenting automation, and policies and practices that encourage employment at older ages could prevent these losses to some degree. VII. Generalizability and the Reallocation of Skills Our estimates suggest that population aging predicts cross-state differences in economic growth. An important advantage of our research design based on differential population aging across states is that it controls for common national shocks. Extrapolating our estimates to explain or predict national trends requires additional considerations. One issue in this context is that the effects of population aging at the state level may be exacerbated or ameliorated by the systematic reallocation of skills across states. An aging population, especially one that is aging in predictable fashion, may induce higher skilled workers to relocate to a state that is aging more slowly. Since this behavior is in response to (predicted) aging, it is part of the causal effect that we capture (unlike changes in elderly share due to confounding factors which also affect local economic growth). However, this type of migration is less likely to occur across countries than within countries, so its role is important to quantify before extrapolating the estimates to the national level. To assess the migration response to population aging, we focus on two outcomes: (1) the fraction of individuals ages with at least a high school degree (as a measure of labor force skill); and (2) the size of the state population (as a measure of migration). We present the estimates in Table 6. We find no statistical relationship between changes in the older share and changes in the skill level of the population. We present estimates using the change in the log fraction with at least a high school degree and, separately, estimates using the change in levels. We do not observe a statistically significant effect for the period as a whole, or in any decade. The point estimates, however, are consistently positive, which suggests that, if 27

29 anything, states that are aging more rapidly become slightly more productive in terms of the observed skill composition of the population ages In the final panel of Table 6, we estimate the effect of aging on changes in state population size. Once again, we find no statistically significant effects for the period as a whole or for any decade, indicating that migration does not react to state-level population aging. The point estimates are positive which is consistent with people migrating to states that are aging more rapidly. Overall, we find little evidence of any systematic migration resulting from population aging which could either increase or decrease the magnitude of our results. VIII. Discussion and Conclusion The fraction of the United States population ages 60 and older will grow by 21% between 2010 and 2020, and by 39% between 2010 and 2050 (Administration on Aging, 2014). This rapid aging of the U.S. population is expected to slow economic growth, place considerable strain on government entitlement programs, and possibly lower per-capita consumption. oting that population aging has been long underway in the U.S., and that changes in the population age structure were largely predetermined by historical trends in the age structure, we use variation in the rate of population aging across U.S. states over the period to estimate the economic impact of aging on growth in state output per capita. Over this time period and across states, we observe substantial variation in population aging, including aging rates comparable to rates forecasted for the United States in the near future. Our estimate of the elasticity of GDP growth with respect to aging is -0.55; that is, a 10% increase in the fraction of the population ages 60+ decreases GDP per capita by 5.5%. This result implies that state-specific differences in population aging can predict important crosssectional differences in economic growth. While we estimate this elasticity using between-state variation, by extrapolating to the national level we gain insight into the potential impact of population aging on national GDP growth. Between 1980 and 2010, the older share increased by 16.8% in the United States. Thus our estimate implies that per capita GDP over the same time period was 9.2% lower than it otherwise would have been absent population aging. This 34 We find similar results when we use changes in the fraction with a college degree or higher instead of changes in the fraction with a high school degree or higher. 28

30 corresponds to a 0.3 percentage point decrease in the annual rate of growth over a time period when the average annual growth rate was 1.88 percent. Between , the older share of the U.S. population is expected to rise by 21%. Thus our estimate indicates population aging will reduce per capita GDP during the current decade by 11.6% relative to a counterfactual in which there is no change in the older share. Annualizing this rate, population aging will be responsible for a 1.2 percentage point reduction in the annual rate of GDP growth, relative to the growth rate with no change in the national share Between , the older population share will rise by 11%, implying a potential reduction in annual growth of 0.6 percentage points. 36 Our estimates are larger in magnitude than those predicted by the ational Research Council (2012). The Council predicted a slowdown in growth in GDP per capita of percentage points per year relative to the long-run rate of 1.88%. The explanation for the difference between our estimate and theirs is that the Council assumed population aging would primarily affect labor force growth and not productivity growth. Our estimate of the effect of population aging on labor force growth alone is similar to their estimate of the total effect of population aging. In fact, for the period, about 2/3 of the total effect of population aging on growth in GDP per capita arose from slower productivity growth, while 1/3 was due to slower labor force growth, with labor supply effects concentrated entirely among older workers. The effect of population aging on productivity growth was driven primarily by changes in human capital, with changes in physical capital and technology playing a minor role. Correspondingly, the reduction in productivity growth was matched by a reduction in wage growth, which points to labor market adjustments that compensate for real losses in the marginal product of labor. The slowdown in productivity growth occurred throughout the age distribution, including younger workers. We interpret this as indicating that older and younger workers are complements in production, and so the productivity of the older workforce affects the productivity of younger workers. This pattern could also arise from a loss of positive productivity spillovers from older 35 Our estimates imply that a 21% increase in the older share would decrease per capita GDP by 11.55%. Define g as the population aging penalty in annual growth rate that results in a 11.55% decrease in per capita GDP 10 years later; let g represent the annual growth rate in the absence of aging. Then, ( ) = (1 + g g ) 10 such that g g Between , the older population share will rise by just 2%. 29

31 to younger workers if productive older workers are more likely to exit the labor force. Our results are also consistent with older workers switching to less productive occupations as they transition into retirement. While we find population aging has had substantial effects on economic growth, it is worth recalling that our estimates do not account for any effects at the national level that may compensate for or exacerbate the slowdown in output growth. 37 Population aging may induce broader general equilibrium effects that we cannot capture in a state-based research design, such as changes in federal tax policy. As a result, our estimates do not preclude even larger effects of population aging on per-capita economic growth in the United States in the coming decades. On the other hand, further improvements in human capital and investments in labor-augmenting technologies, coupled with greater labor force participation at older ages could temper these effects, as well as reduce the magnitude of changes in federal tax policy that will be required to address them. References Acemoglu, D., & Restrepo, P. (2018). Demographics and automation (o. w24421). ational Bureau of Economic Research. Administration on Aging (2014). Projected Future Growth of the Older Population. U.S. Department of Health and Human Services. (accessed on October 3, 2014). Aiyar, Shekhar, Christian Ebeke, and Xiaobo Shao (2016). The Impact of Workforce Aging on Euro Area Productivity. IMF Euro Area Policies, July, Aksoy, Yunus, Henrique S. Basso, Tobias Grasl and Ron P. Smith (2015). Demographic Structure and Macroeconomic Trends, Manuscript, available on REPEC Arellano, Manuel and Stephen Bond (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. The Review of Economic Studies, 58(2), Barro, Robert J and Xavier Sala-i-Martin (1992). Convergence. Journal of Political Economy, 100(2), The ational Research Council also did not account for general equilibrium effects of population aging on the federal budget that might lead to changes in tax policy, so this is not a source of difference between our estimate and their forecast. 30

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35 Figures Figure 1: Percent of United States Population Age 60+: Actual and Projected % 25.0% 20.0% 15.0% 10.0% 5.0% 0.0% Age Age Age Age 85 and older Source: U.S. Census Bureau, compiled by U.S. Administration on Aging. 34