Aging and Asset Prices

This study quantifies the potential effects of aging on asset prices using a sophisticated overlapping generations (OLG) model with international diversification reflecting the global nature of capital markets. We show that the expected decline in the returns to capital will depend on the degree of international diversification. In the case of optimal diversification within the EU returns will drop by around one percentage point until 2035. The increasing risk aversion of an aging society will lead to differential effects on the returns on stocks and on bonds. We estimate the equity premium to rise by around 70 base points over the next 25 years. The sector that will be affected most by the demographic trend will be returns on real estate, however, only in the very long term. The main insight is that household size lags population size by about 20 years. One reason is that an older society features a smaller household size and thus, ceteris paribus, more households. Hence, housing demand will only begin to fall from 2025 onwards even if populations start declining today. Taken all evidence together, capital markets are not immune to demography. Rates of return will decline in response to demographic forces, but only very moderately. There is no scientific reason to assume that a major “asset meltdown” will occur when the babyboom generation retires.

Trends in German households’ portfolio behavior - assessing the importance of age- and cohort-effects

We start out from a comparison of aggregate trends in German households’ portfolio shares and participation rates as they derive from micro data and from the National Accounts. We find the broad trends supported by both data sources. By international comparison the portfolio share of safe investments with banks in Germany has always been high. It is continuously and strongly declining though. Life insurance has gained substantial importance since the 1960s. In the 1990s it lost some of its previous dominance with the rise of stocks and mutual funds. We find that the popularity of mutual funds continued through the stock market downturn. The baisse caused rather few investors to finally quit on direct investments in the stock market. Looking at the underlying developments at the age- and cohort-level, we aim to compare empirical life-cycle trajectories with the implications of theoretical models and assess the importance of age- and cohort-effects in the observed aggregate trends. We find the rising importance of securities as well as the declining share of saving accounts to be prominent at almost all ages. We observe a declining importance of life insurance for the oldest cohorts and – somewhat surprisingly – for the youngest cohorts. Last, we use a decomposition of the observed trends into age- and cohort-effects and highlight the crucial assumptions that there is a unique age-profile and cohort differences all take the form of shifts to this age-profile. We argue that both assumptions might well be at odds with theoretical considerations and therefore harm the desired interpretation.

Understanding the trends in income, consumption and wealth inequality and how important are life-cycle effects?

Rising inequality in income, wealth and consumption has received a good deal of public attention in the past years. At the same time, also macroeconomists are more and more interested in inequality as they have expanded their models to incorporate heterogeneity in the household sector. We supply these models with empirical benchmarks for their calibration and contribute to the understanding of the reasons underlying the trends in inequality. Specifically, we employ a variance decomposition and estimate life-cycle profiles of inequality in income, consumption and wealth based on two measures of inequality. We deepen the discussion on wealth inequality by evaluating the relative importance of savings, portfolio choice and inheritances for the accumulation of wealth. To do so, we project active and passive savings based on the observed saving and investment behavior of synthetic cohorts from the German Income and Expenditure Survey (EVS).

Savings motives and the effectiveness of tax incentives – an analysis based on the demand for life insurance in Germany

We exploit data on German households’ savings in life insurance products, the characteristics of life insurance products and the specific tax treatment of savings in life insurance products to assess the importance of different savings motives and the effectiveness of tax incentives. Our insights about the determinants of the demand for life insurance products also allow a broad assessment of the possible consequences from the recent reforms of the pension system and of the tax treatment of life insurance policies. Socioeconomic and institutional factors generate substantial variation within the population and over time, e.g. in the replacement rates of the public pension system and the household tax rates, which allows us to disentangle savings motives and the effects of tax incentives from other factors. We employ a number of indicators for the different savings motives. Further, based on the specifics of the German tax law and the richness of our data we are able to generate a unique measure of possible tax savings associated with savings in life insurance products. We find support for our hypothesis that savings in life insurance products may substitute for a low replacement rate in the public pension system. Only high income households who face lower replacement rates from the public pension system do not increase their demand for life insurance products. Further, we use several measures for a possible bequest or family insurance motive. Our evidence on the relevance of such savings motives is mixed like the existing literature. The presence of a family increases the demand for term life insurance but households with children do not accumulate higher levels of life insurance wealth. Further, some income inequality within a couple increases the likelihood to save in life insurance. The effects are not increasing in the degree of income inequality though and only partly significant. Finally, we find households with high tax rates to be more likely to invest in life insurance products, indicating that the tax free interest earnings from a long term insurance contract play a strong role in households’ choice to invest in life insurance. The possibility to deduct contributions from taxable income turns out to be no incentive to save in life insurance products.

Diffusion Mean Estimation on the Diagonal of Product Manifolds

Computing sample means on Riemannian manifolds is typically computationally costly as exemplified by computation of the Fr\'echet mean which often requires finding minimizing geodesics to each data point for each step of an iterative optimization scheme. When closed-form expressions for geodesics are not available, this leads to a nested optimization problem that is costly to solve. The implied computational cost impacts applications in both geometric statistics and in geometric deep learning. The weighted diffusion mean offers an alternative to the weighted Fr\'echet mean. We show how the diffusion mean and the weighted diffusion mean can be estimated with a stochastic simulation scheme that does not require nested optimization. We achieve this by conditioning a Brownian motion in a product manifold to hit the diagonal at a predetermined time. We develop the theoretical foundation for the sampling-based mean estimation, we develop two simulation schemes, and we demonstrate the applicability of the method with examples of sampled means on two manifolds

Simulation of Conditioned Semimartingales on Riemannian Manifolds

We present a scheme for simulating conditioned semimartingales taking values in Riemannian manifolds. Extending the guided bridge proposal approach used for simulating Euclidean bridges, the scheme replaces the drift of the conditioned process with an approximation in terms of a scaled radial vector field. This handles the fact that transition densities are generally intractable on geometric spaces. We prove the validity of the scheme by a change of measure argument, and we show how the resulting guided processes can be used in importance sampling and for approximating the density of the unconditioned process. The scheme is used for numerically simulating bridges on two- and three-dimensional manifolds, for approximating otherwise intractable transition densities, and for estimating the diffusion mean of sampled geometric data

Aging and asset prices

This study quantifies the potential effects of aging on asset prices using a sophisticated overlapping generations (OLG) model with international diversification reflecting the global nature of capital markets. We show that the expected decline in the returns to capital will depend on the degree of international diversification. In the case of optimal diversification within the EU returns will drop by around one percentage point until 2035. The increasing risk aversion of an aging society will lead to differential effects on the returns on stocks and on bonds. We estimate the equity premium to rise by around 70 base points over the next 25 years. The sector that will be affected most by the demographic trend will be returns on real estate, however, only in the very long term. The main insight is that household size lags population size by about 20 years. One reason is that an older society features a smaller household size and thus, ceteris paribus, more households. Hence, housing demand will only begin to fall from 2025 onwards even if populations start declining today. Taken all evidence together, capital markets are not immune to demography. Rates of return will decline in response to demographic forces, but only very moderately. There is no scientific reason to assume that a major “asset meltdown” will occur when the babyboom generation retires

Aspects of savings, wealth, portfolio choice, and inequality in the life-cycles of German households

The first chapter investigates life-cycle saving behavior with a focus on the elderly, who are frequently found to continue saving after retirement. We test the reliability of this evidence, as it is in many cases based on repeated cross-sectional data, where we cannot directly control the stability of the sample. In fact, differential mortality or differential sampling success may lead to biased age trajectories in savings and wealth. Exploiting a characteristic of the German pension system, we find evidence for differential mortality with respect to permanent income in the German Income and Expenditure Survey (EVS) – thereby confirming previous studies. Correcting the age-trajectories of savings and wealth for the resulting sample bias, we do not find evidence supporting the hypothesis that the German savings puzzle may be a statistical artifact resulting from the use of a synthetic panel. The second chapter analyses historical trends in household portfolio choice and investigates the importance of age-, cohort- and time-effects. We show based on a range of cohort-analyses, that all three effects matter in the context of household portfolios. In the following, we focus on the age-pattern of the different portfolio components and find them in line with what we would expect given the savings motives which we would attribute to the respective assets. Apart from the empirical results, we highlight methodological issues around the estimation of life-cycle profiles. The plain assumption that there is a common life-cycle pattern may be false. Cohorts must be expected to differ in preferences, expectations, and initial endowments. Further, the institutional environment may change. Each of these factors may change the shape of the life-cycle profile across cohorts. Hence, the assumption of an unchanged age-profile may lead to biased results. We thus recommend the use of plain cohort-analyses which also convey substantially more information about the changing nature of life-cycle profiles. In chapter three, we examine in detail the determinants of the demand for life-insurance products. Their capacity to satisfy a wide range of saving motives should provide important insights beyond the demand for life insurance itself. Cross-sectional and time variation in the tax treatment towards life-insurance allows a dedicated focus on the importance of tax-effects. The tax exemption for interest earned in a long-run life-insurance contract turns out a distinct investment motive. The possibility to deduct contributions from taxable income, however, turns out ineffective. Further, we find overall supportive evidence for the old-age saving motive. The wish to provide for ones dependents is associated with higher investments in products with a term-life component. Our results imply that the cutbacks in the public pension system and the recent reform of the tax incentive scheme should promote annuity insurance products at the disadvantage of whole life insurance products. The fourth chapter is dedicated to the analysis of inequality in a life-cycle context. Over the last 25 years, Germany has experienced little growth in income and consumption inequality, whereas wealth inequality has grown significantly. Decomposing these trends we illustrate the influence of the German Reunification and the trend towards smaller households. Next, we look at the evolution of in inequality over age and find ambiguous results for income and wealth and a clear upward trend in consumption inequality over age. Finally, we further investigate the drivers behind wealth inequality. Active savings contribute the lion’s share of wealth growth in Germany. Passive savings, by contrast, have mostly caused wealth reductions. The reasons are the conservative asset allocation of financial wealth, as well as the poor performance of real estate wealth. The predominance of active savings for wealth growth implies a strong interdependence between the distributions of wealth and income in Germany. The concluding chapter documents all imputation and harmonization work which was involved in the preparation of the EVS data. We make two important conceptual contributions: First, we suggest an improved imputation approach for the EVS wealth data which ensures a better preservation of the variation within the imputed variables and the interdependencies between variables. Second, we assess the possible influence of structural changes to the EVS sample on life-cycle analyses, specifically the switch from an annual to a quarterly household diary and the changing sampling threshold with respect to income