The aim of this thesis is to analyze the consequences of a stochastic population growth on the equity premium in an overlapping generations (OLG) model. This to see if this stochastic variable can account for part of the Equity Premium Puzzle. The population in an economy changes due to births, deaths and migration. The risks of demographic change, here interpreted as fertility risk, resulting in a baby boom or a baby bust, may be significant and it is not insurable in the market. Thus fertility risk requires a premium to be born. As documented by Davis and Li (2003), the patterns of the elderly dependency ratio are largely a consequence of changes in fertility, although longevity are also important.
The model incorporates a stochastic growth production sector. Economic growth is exogenous. Asset returns are determined by time preference, the marginal utility of wealth and attitudes toward risk. In the case of a small open economy, the asset returns are determined independently of the rate of growth, but in a closed or in a large open economy, they may be linked.
The idea is motivated by the assertion that the entry of the baby boom generation, those born roughly in the two decades following World War II, into its peak saving years was a key explanatory factor in the rise of stock market values in the 1990s. Examples are Passell (1996) and Moon et. al. (1998). Individuals aged 40 to 60 years old are the prime savers in the economy in the US. That prices of stocks and other real assets are bid up are accompanied by the prediction that when the Baby Boomers reach retirement, they start consuming their savings (selling their assets) which result in declining asset prices and increasing expected returns.
Population (forecasts) are widely used in various planning situations, such as schooling, health care and pension systems. In the very short run, the uncertainty expressed by stochastic forecasts is limited. On a five-year planning horizon you may safely use a deterministic forecast. In the long run however, planners interested in the age structure of the population 30 or more into the future, should take uncertainty into account.
Contents
Introduction
1. Expected Utility Framework
- Risk Aversion
Asset Pricing
Consumption-Based Capital Asset Pricing, the CCPM
The Equity Premium Puzzle
Overlapping Generations Models
Equity Premium and Population
2. Diamond Model with Log-normally Distributed Population Growth and Productivity Growth
- Assumptions
The Model
Stochastic Population
The Stochastic Production Sector
Households
Equilibrium Capital Accumulation
Marginal Product of Capital
The Riskless Rate
Equity Premium
3. Calibration
- The Case of Norway
The case of the US
Analysis
Conclusion
Appendix
Bibliography
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