Life-cycle hypothesis

The life-cycle hypothesis (also: life cycle theory or life -time income hypothesis) is a term used in economics and is a basic theory for individual and overall economic savings. The most important aspect is the importance of saving and borrowing for the transfer of resources (income ) over the lifetime of an individual. Developed by Franco Modigliani, this theory of consumption is in addition to the relative income hypothesis of Duesenberry James and the permanent income hypothesis of Milton Friedman also deals with the long-term consumption function. All of these approaches relate to empirical studies on the short-and long -term consumption function, the decline in particular Simon Kuznets.

The life-cycle theory is clear from the assumption that every individual is trying to keep its standard of living over the entire life time stable. Thus, an individual does not relate his consumption and saving behavior, as assumed in the consumption function, each on a period and the resulting disposable income, but long-term planning for all periods to distribute their own consumption as possible for the entire lifetime.

It is assumed that the average income of a consumer is almost constant at long- term perspective. Thus, short-term changes in the level of income over the lifetime of an individual do not matter.

History of Theory

In the 1950s, Modigliani examined in collaboration with Richard Brumberg and Albert Ando, the consumption function. Together they developed in several fundamental papers today's life-cycle hypothesis of saving and consumption. Basis of the investigations was the model of household behavior by Irving Fisher. The aim was to elucidate the contradictions that showed with empirical data in connecting the Keynesian consumption function. Fisher's model assumed that the consumption of an individual depends on his lifetime earnings. Modigliani refined this statement and stressed that a person's income is subject to constant changes in the course of their lives. However, the savings that will be gained through savings in times of higher income, are moved to lower income segments of life. This assumption about consumer behavior served as the basis for the life-cycle hypothesis.

The modern theory of consumption is a fusion of the life cycle theory of Franco Modigliani and the permanent income theory of Milton Friedman, because both basic theories resemble very much. This combined theory is referred to by economists as a life-cycle permanent income hypothesis. Modigliani represents thereby the Keynesian approach, Friedman modern monetarism.

1985 Modigliani was awarded for his work on the life-cycle hypothesis with the Nobel Prize in Economics.

The life-cycle hypothesis serves as an argument for private pension provision against a PAYG. The PAYG burden a household according to income evenly over the working lifetimes and is contrary to the natural course of saving, so small savings in the early acquisition time, then high savings in advanced labor, finally at the age low savings or Entsparnis. In contrast, the life-cycle hypothesis has been criticized for a lack of consideration of unequal income and other savings motives addition to retirement, as there would be precautionary savings, saving for children's education, gaining independence from current income, among other things

Representation and delimitation

The life cycle theory considers how a consumer keeps stable standard of living during his lifetime, although his income changes. It is implied that a typical individual in the first period of life ( childhood, adolescence ) has a very low income and must fall back during training on loans ( dissaving ) in order to achieve the desired lifestyle. In the subsequent active employment income increases ever more and then for capital formation (savings ) and repayment of loans used. In the retirement phase, the income is again lower ( pension ) and it is on the accumulated wealth resorted ( dissaving ). At the end of life ( at the optimum time of death ) the accrued during the lifetime of assets is fully depleted, ie, saving and dissaving cancel. This simplified model assumes that the individual received any inheritances and gifts during his lifetime, and has amassed neither debt nor fortune.

The permanent income theory predicts, however, what income the consumer is .. The empirical relevance of the life cycle theory is very controversial available over its lifetime. Some authors refer to it as "extremely unrealistic " while the widely accepted practice of seniority (rising payment by professional or age) supports the hypothesis.

Derivation

With respect to a consumer assumes the following:

• He has yet to live T years
• His fortune amounts to the height W
• He expects to end of life nor an income Y
• It will still function R years and then retires from the labor force from

For simplicity it is further assumed that the interest rate (and thus interest income from savings ) is zero. The amount, which is now available to the consumer derives from its capacity W and his lifetime earnings (R * Y). This is the amount the consumer can distribute his remaining years of life T. The life-cycle hypothesis implies now that the consumer 's consumption over this period T smoothes, so divides the available amount in equal parts.

By rearranging this equation, we obtain the following consumption function for the consumer:

The aggregate macroeconomic consumption function is then

α with the marginal propensity to consume out of wealth and the marginal propensity to consume out of income β.

Mathematical example

The life-cycle hypothesis is a dynamic microeconomic partial model with a finite time horizon T. In it, a single individual is maximizing utility. The utility function has the usual neoclassical assumptions. It contains no inheritance motive. The benefit of future periods is simplified for the benefit of today's period equal valued (no subjective time discount). The individual has his life a constant labor income e, retirement is not subject to simplified. The assets of V generated the interest rate r. The calculus is then: Maximize the utility function

Specifically

Subject to the constraints

After formation of the Lagrangian approach, the application of the Kuhn- Tucker conditions and the partial derivative with respect to and, after the calculation of consumption each period as a result of the following saving function

Normalizes and discounted to the first period is the

Stands for the consumption of the first period and is a fixed number, depending on interest rates and income. Savings over the life Discounting is always lower. The consumption increases with the rate of the capital market interest rate in this model. As always greater than in the normalized equation of the subtractor over time is increasing, and this will reduce the savings. For large interest rates you may initially see an increase in the savings ratio in undiscounted model. Discounted these values ​​but at the beginning of the life cycle calculus down, these are always lower.