How Does the Age Structure Affect Local Economies in the US?

This study examines the impacts of population aging on a wide range of economic indicators from a regional perspective. Many countries, including the United States, are experiencing demographic aging. This may have a dramatic impact on both the national and sub-national economies. However, there is little consensus about its impact on local sub-national economies. This study uses regional variation in age structure to explain economic outcomes at the metropolitan statistical areas (MSAs) level. In order to identify causal effects, Mahalanobis distances were calculated to identify the matched cities as instrumental variables. The study finds that regions with older age structures tend to have higher growth rates of GDP per capita and lower growth rates of unemployment, but such positive effects are likely to fade away in the long run. Additionally, there is no significant impact of age composition on income. The choice of variables is critical as it can lead to mixed results. The results are robust before, during and after the economic recession. Quantile regression is also used to explore potential heterogeneous effects among MSAs. The results show that MSAs, regardless of their size, are uniformly affected by the age structure.


INTRODUCTION
"With every mouth God sends a pair of hands." This old saying provides a good starting point for thinking about the impact of population on economic growth. Demographic changes not only affect the consumption needs of an economy (the number of mouths), but also affect the productive capacity of the economy (the number of hands). Many countries are seeing their creative output (Jones, 2010). On the other hand, the elderly can still make a significant contribution to the economy, such as taking care of grandchildren and volunteering, although this will not be reflected in many economic statistics since these activities often do not involve monetary payments (Bloom et al., 2007). Thus, it is essential to examine the net effects on the supply side.
On the demand side, although the dissaving by the elderly can reduce the saving rates and harm the economy (Amaglobeli et al., 2019), the net impacts on consumer demand is unknown, because the age structure alters the product composition of consumer demand. For example, the elderly population could shift the demand from education to healthcare, but the net effect of these demand shifts could go either way (Assadian, 1995;Hock and Weil, 2012). Therefore, population aging can have both positive and negative impacts on both the demand and supply sides.
In summary, the relationship between age variables and economic outcomes is complicated. Although previous research has built models to explain the complicated mechanism, empirical evidence is still rare. One main reason is the challenge of dealing with the endogeneity of age structures (Prettner, 2013). Most existing empirical studies explore the age effect on the economy using either individual-level data or international comparison. However, the regional variation of age compositions within a country is largely ignored 1 . This regional approach can provide additional insights, as the confounding effect of cultural and legal differences in retirement age across national borders will not distort the results.
Drawing on the discussion above, this study aims to examine the effects of age compositions on US MSAs. To identify causal effects, the IV-matching technique is used to find suitable instrument variables. The results are robust under different specifications, and lead to the conclusion that regions with older structure tend to have relatively faster growth of GDP per capita and slower growth of unemployment, although such positive effects are likely to fade away in the long run.

EMPIRICAL ANALYSIS
The basic unit of analysis is the metropolitan statistical areas (MSAs) because they provide a good measure of functional economic areas. MSAs are designed explicitly by capturing local labor markets with at least 25% commuting between counties and the principal core of metro areas (Partridge et al., 2017). County-level data are not used in this study due to availability, as the Bureau of Economic Analysis only publishes GDP data at the state and MSA levels.

Explanatory Variable: Degree of Population Aging
The key variables of interest measure the relative size of the aging population in the US MSAs. Specifically, four proxies -the median age, share of prime-age (25-54 years old) workers, senior dependency ratio and the share of senior population will be used to measure the age structures across MSAs.
The first explanatory variable is "median age." This is a good measure in that it can represent the age distribution of the total population. However, this measure would be less effective in evaluating labor market effects, because it is affected by the number of children who have not yet entered the labor market. The table below provides an example showing the regional variation of median ages among MSAs (only the top five and the bottom five are listed): The second variable, "share of prime-age population," is defined as the fraction of people between 25 and 54 years old. Compared with the entire "working-age population" (defined by the U.S. Department of Labor as those between 16 and 64 years old), prime-age population has several favorable traits. One advantage is prime-age workers have not entered the retirement age window and still have strong incentives to stay in the labor force. Another advantage is that the prime-age population tends to earn more, because most high school and college students are excluded. This is a good measure of "population dividend," as it represents the most productive age group.
The third variable "the share of old population" is defined as the fraction of people above 65 years old. One advantage of this operational definition is the consistency with the concept of "population aging" as defined by OECD 2 . Another advantage is that this operational definition can largely represent the pensionable population. Social security's full-benefit retirement age is gradually increasing because of legislation passed by Congress in 1983. Based on the legislation, most people aged 65 years or older during the study period 2003-2014 would have the opportunity to retire without compromising their benefits 3 . Thus, the labor supply of this cohort was not affected by the pension concerns.
The fourth variable is the "senior dependency ratio". This ratio compares the number of people above 65 years old to the working age population. The denominator differs from the whole population in that the youth dependents are deducted from the denominator. Thus, only the economically active population are included in the calculation, which yields a more precise picture of "dependency" defined by age. The lower values may underscore greater financial pressures on the social security system.
In summary, all four proxies capture different aspects of the changing workforce and total population. Any single indicator may contain significant measurement errors which leads to estimation errors. Thus, all proxies will be examined in the following analysis in order to give a full picture of population aging's impact. The chart below displays the age composition of the US population since 2005: 3.2. Dependent Variable: Economic Growth, Labor Market Outcomes and Incomes A wide range of economic indicators which evaluate different aspects of the overall economic performance is used as dependent variables. To measure the regional economic growth, I obtained MSA-level GDP data in 2005-2015 from the Bureau of Economic Analysis. Both GDP per capita (the measure of well-being) and GDP per worker (the measure of productivity) were calculated. To measure labor market outcomes, I also collected indicators such as labor force participation rate, unemployment rate and the number of jobs at the MSA level from the American Community Survey and the Bureau of Economic Analysis. The annual growth rate was calculated to measure the short-term effects, while the 10-year change rate was used to gauge the long-term effects. To account for only labor force effects, the population aged 18 or less will be excluded from the denominator when calculating per capita GDP; therefore the number of dependent children will not distort the labor market ratios. The trends of economic variables from 2005 to 2015 are displayed in Figure A.1.

Model
The basic model takes the following form: where Y is a range of key economic indicators including GDP growth, labor market outcomes and personal incomes; ∆Y represents the change rate of these economic variables in the short run (1 year) and the long run (10 years); α is the coefficient before the age structure variables, which is the main coefficient of interest; β j is the state fixed effects, which control for timeinvariant characteristics of each state; Z i,t is a vector of time-varying covariates including demographic factors other than age, including education, gender and race compositions of the population in one MSA in a given year. The residual is represented by , and robust standard errors are reported in the results tables. Physical capital is also an important factor in most production functions. However, since no useful government statistics on MSA-level capital investment can be found at this time, this model assumes that the production technology, as well as the capital/labor ratio, is the same across MSAs. Therefore, the rate of return is equalized across the country. This is an appropriate assumption inside a domestic economy with highly mobile capital.
One important empirical challenge in estimating the effects is the endogeneity of the age structure. Potential confounders remain after controlling for time and state fixed effects, which could invalidate the causal relationship, since the age composition of the local population may be endogenous itself. For example, younger people are more likely to be attracted by places where there is a vital labor market with many opportunities, while places full of energetic younger people are more likely to have better economic performance. To account for these and other factors driving both the degree of population aging and the economic performance in MSAs, I use an "IV-matching" strategy to identify instrumental variables (Zhang et al., 2020). Specifically, the Mahalanobis distance will be calculated for each MSA pair to determine their best matches based on economic and demographic statistics in 2005: where N characteristics of MSAs will be used to calculate the distance between MSA X and MSA Y; s i is the standard error of trait i.For example, the median age of the MSA with the smallest Mahalanobis distance will be used as an instrumental variable for the MSA of study. The calculation of Mahalanobis distance includes population size, sex ratio, share of white population and share of population with at least a Bachelor's degree. To prevent any spatial spillover effects, the matched MSA cannot be in the same state as the original MSA 5 . Since the boundaries of each MSA are based on the commuting between counties, the spatial spillover effects between nearby MSAs should not be a major issue. Descriptive statistics show that those variables chosen as criteria are highly correlated with age compositions, and their correlation is reported in Table A.2. The first stage F-statistics are also reported showing a strong association between instruments and the endogenous age structure variables.

Short-Term Effects
In this subsection, the impacts of population aging on annual changes of economic variables are examined. I begin by estimating ordinary least square (OLS) regressions to explore the relationship between age profiles and economic outcomes. The results are presented in Table  A.3. From these results we can see that GDP growth rates are generally not associated with age composition. However, after controlling for the population size, MSAs with older age structures tend to have a higher growth rate of GDP per worker and GDP per capita. Regarding local labor markets, it was surprising to find that labor force participation rates are not affected by age compositions. Additionally, older age structures are likely to cause a slower growth of unemployment rates, and the results on non-farm and farm jobs are mixed. None of the four variables representing age structures was significantly associated with the growth rate of income variables. As discussed in section 3, a matching strategy based on Mahalanobis distance was used to identify the instrumental variable for the age structures to address endogeneity. This model is the preferred approach for short-run effects, and the results are reported in Table A.4. The findings from the 2SLS models are generally consistent with those in the OLS models. First-stage F-statistics are reported and indicate no concerns about weak instruments.

Long-Term Effects
In this subsection, I examine the impacts of population aging's level on ten-year changes of economic variables. Other than short-run effects (annual growth rates), this study also looks at long-term effects (10-year change rates). The OLS results are presented in Table  A.5. In the long run, MSAs with older age structures tend to have a slower GDP growth rate. However, such detrimental effects were not statistically significant after controlling for the population size. The 10-year growth of both labor-force participation rates and unemployment rates are not affected by age compositions. But the increase in median age and the share of population above 65 years old are likely to decrease total number of jobs, which is largely driven by the decrease in non-farm jobs. In terms of income measures, income per capita and mean income for full-time workers are not significantly influenced by age structures. However, increase in median age, senior dependency ratio and the proportion of elderly population is likely to reduce the 10-year growth rate of median incomes for people above 25 years old.
A matching strategy was also used to identify suitable instrumental variables, and it is the preferred model for long-run effects. 6 The results of the 2SLS model are reported in Table A.6. Based on the results, the afore-mentioned effects are all gone after instrumenting for the age structure variable, suggesting that the short-term impacts of age compositions on local economy are likely to fade away in the long run.

Time-Differenced Effects
In this subsection, the time-differenced OLS and 2SLS regressions of the following form are estimated: where ∆X includes the change rate of age structure in both short-term (1-year) and longterm (10-year). The motivation is that some MSAs may have extremely young or old age structures, which could affect their long-run performance. If that is the case, then simply using the level of population aging would not fully capture the effect. Furthermore, timedifferenced regressions will remove time-invariant factors that potentially affect both age compositions and economic outcomes (Rickman et. al, 2015). Notice, however, that the control variables are not time-differenced due to the possible endogeneity.
The results of the short-term and long-term time-differenced OLS models are reported in Table A.7 and Table A.8 respectively. Because the major explanatory variable are now the "rate of changes" rather than the "level," the interpretation will be different. Based on the short-term results, the MSAs that are getting older tend to have slower growth of GDP and GDP per capita. In terms of the local labor market performance, those MSAs are also more likely to experience a decline in labor-force participation rates, non-farm jobs as well as total number of jobs. Although the growth rate of incomes is found to be not affected by the level of population aging, it is significantly impacted by the speed of aging. The findings show that those MSAs which are turning older will have reduced growth rates of income per capita and median income for people above 25 years old. These findings are consistent across all four indicators of age structures. The long-run OLS results are reported in Table A.8, and similar patterns are found for the time-difference models when 10-year growth rates are examined.
The results of short-term and long-term time-differenced 2SLS models are reported in Table A.9 and Table A.10 respectively. It can be seen that the portion of prime-age workers is still significant when using instrumental variables. In the short run, regions with a growing prime-age population tend to have higher growth rate of GDP per capita, labor-force participation rate and personal incomes. However, such positive effects tend to fade away in the long run, because none of the coefficients are statistically significant when examining ten-year changes.

Robustness Check
As a robustness check, the study period was divided into three groups: 2005-2007, 2007-2009 and 2009-2015. This allows testing for potential heterogeneous effects across different stages in the business cycle. It is possible that the effects specific to the Great Recession may be distorting the results. Thus, are economic consequences of population aging different before, during and after the recession? Specifically, OLS models are used to examine the impacts of age structures on local economy before, during and after economic recessions, 7 and the detailed results are reported in Table A.11, Table A.12 and Table A.13 respectively. However, the results across the business cycle were consistent with the earlier findings. There were no significantly different effects of age structures due to the business cycle.
As another robustness check, quantile regressions were used to test for potential differing effects of age compositions across MSAs with different sizes. The quantile regression approach can provide flexibility for modeling data with heterogeneous conditional distributions (Koenker and Hallock, 2001) and it allows for heterogeneous effects on outcome variables across the spectrum of all quantiles. Thus, I ran a series of quantile regressions using GDP per capita and unemployment rates as dependent variables, respectively, because these two indicators are consistently significant in most model settings. The coefficients of age compositions in short-run models are reported in Figure  These graphs illustrate how the effects of age structures vary over quantiles, and how the effects at various quantiles differ from the OLS coefficients. On the plots of coefficients, it can be clearly seen that the difference in effects among quantiles is negligible. The median estimates are also very close to the OLS point estimates, lying within the confidence interval of OLS estimates. Thus, the results cannot reject the equality of estimated coefficients over different quantiles.

CONCLUSIONS
This study examines the impacts of population aging on local economies using a wide range of variables, including ten economic outcome variables and four age structure variables. Both rate and level measures are examined using OLS and 2SLS regressions to find the most consistent results. Based on the above results, several conclusions can be drawn. First, age composition does not have significant impacts on the personal income of the locals. Second, in the short run, older age structures tend to have positive effects on the local economy, leading to a higher growth rate of GDP after controlling for population and a slower growth of unemployment rates. Thirdly, aforementioned positive effects are likely to fade away in the long run. The conclusions above also demonstrate the importance of choosing multiple indicators, as not all aspects of local economies are uniformly affected by all aspects of age structure. Lastly, MSAs, regardless of the size of the local economy, are almost uniformly affected by age compositions. Results from quantile regressions cannot reject the equality of coefficients before the age variables.
This study builds on the previous literature while making the following three main contributions. First, previous studies on population aging only provide evidence at the state level or on international comparison. This paper specifically focuses on MSA-level data, exploring the impact of demographic aging using a finer-solution level. Studying MSAs rather than states removes remote rural counties which presented a confounding factor, because rural demographics can be very different from urban areas. Second, this study uses more than one proxy for the degree of population aging and evaluates a wide spectrum of economic indicators. This captures a more complete picture of the economic dynamics of aging. Lastly, this study attempts to find new instrumental variables to address the endogeneity concern of age structure. This study has two major implications for policy makers and academic researchers. First, this paper cautions local government that the potential impacts of demographic shifts could affect local economy. However, aging's impacts on local economy are mixed, and one-sizefits-all policy cannot address future demographic changes. Second, this paper cautions future studies about choosing the indicators for age structures and the measure for economic outcomes, because different choices of variables could lead to quite different results as shown in this study. A new economic measure that can include the non-market contribution of the elderly is also preferred.
Some meaningful questions about population aging's impacts on local economy remain to be answered. One line of research is to make out-of-sample predictions. Specifically, historical data can be employed to gauge the key coefficients, which represent the relationship between population aging and local economy. Thus, these coefficients can used to predict future economic performance. Another line of future research will focus on the decomposition of population aging, which results from both declining mortality and declining fertility. Theoretical models have demonstrated the potential differing impacts of these two factors. However, this empirical study cannot explore how the impact is decomposed by these two ©Southern Regional Science Association 2021.
factors without MSA-level data on mortality and fertility. Lastly, the channels through which age affects the local economy still need to be examined. Future research can take a closer look at either demand or supply with local spending data.
2. Standard errors, which are robust to heteroskedasticity, are reported in parenthesis.
3. The numbers of observations are different due to missing data.
2. Standard errors, which are robust to heteroskedasticity, are reported in parenthesis.
3. The numbers of observations are different due to missing data.
2. Standard errors, which are robust to heteroskedasticity, are reported in parenthesis.
2. Standard errors, which are robust to heteroskedasticity, are reported in parenthesis.
3. The numbers of observations are different due to missing data.
2. Standard errors, which are robust to heteroskedasticity, are reported in parenthesis.
3. The numbers of observations are different due to missing data.
2. Standard errors, which are robust to heteroskedasticity, are reported in parenthesis.
3. The numbers of observations are different due to missing data.
2. Standard errors, which are robust to heteroskedasticity, are reported in parenthesis.
2. Standard errors, which are robust to heteroskedasticity, are reported in parenthesis.
3. The numbers of observations are different due to missing data.