Life cycle hypothesis

Basic idea of ​​saving behavior in the life cycle according to Modigliani (extremely simplified reality); based on Freess, Tibitanzl; Macroeconomics , Munich, 1994, p. 60.

Life cycle consumption function; Consumption depends on wealth and income; based on Mankiw; Macroeconomics , Stuttgart, 2000, p. 498.

Shift in the consumption function due to changes in wealth (here: increase in wealth); based on Mankiw; Macroeconomics , Stuttgart, 2000, p. 498.

Consumption, income and wealth during the life cycle; based on Mankiw; Macroeconomics , Stuttgart, 2000, p. 499.

The life cycle hypothesis (also: life cycle theory or lifetime income hypothesis) is a term from economics and is a fundamental theory for individual and macroeconomic saving. 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 consumption theory, in addition to the relative income hypothesis of James Duesenberry and the permanent income hypothesis of Milton Friedman, also deals with the long-term consumption function. All of the approaches mentioned refer to empirical studies of the short and long-term consumer function, which go back in particular to Simon Kuznets . Kuznets noticed a significant discrepancy between American consumption and savings behavior compared to Keynes' forecasts.

The life cycle theory arises from the assumption that every individual tries to keep his standard of living stable over his entire lifetime. Thus, an individual does not relate his consumption and saving behavior to a period and the income available with it, as assumed with the consumption function, but rather plans long-term over all periods in order to distribute his own consumption as best as possible over the entire lifetime.

It is assumed that a consumer's average income is almost constant over the long term. Thus, short-term changes in income levels over an individual's lifetime do not play a role.

History of theory

In the 1950s, Modigliani studied consumption function in collaboration with Richard Brumberg and Albert Ando . Together, in several fundamental essays, they developed today's life cycle hypothesis of saving and consumption. Irving Fisher's household behavior model formed the basis of the research . The aim was to clear up the contradictions that emerged when the Keynesian consumption function was linked to empirical data. Fisher's model assumed that an individual's consumption was dependent on his lifetime income. Modigliani refined this statement, emphasizing that a person's income is subject to constant changes throughout their life. However, the savings made by saving during periods of higher income can be shifted to periods of lower income. This assumption regarding consumer behavior served as the basis for the life cycle hypothesis.

Modern consumption theory is a fusion of the life cycle theory of Franco Modigliani and the permanent income theory of Milton Friedman, as both basic theories are very similar. This combined theory is also referred to by economists as the life cycle permanent income hypothesis. Modigliani represents the Keynesian approach, Friedman the modern monetarism.

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

The life cycle hypothesis serves as an argument for private old-age provision against a pay-as-you-go system . The pay-as-you-go system burdens a household evenly according to income throughout working life and is in contradiction to the natural saving process, i.e. low savings in early working life, then high savings in advanced working life, and finally low savings or savings in old age. On the other hand, the life cycle hypothesis is criticized for not taking into account unequal incomes and other savings motives besides old-age provision, such as precautionary savings, saving for child education, gaining independence from current income, etc. a.

Representation and demarcation

Life cycle theory looks at how a consumer keeps their standard of living stable throughout their lifetime, even if their income changes. It is implied that a typical individual has a very low income in the first phase of life (childhood, adolescence) and also has to fall back on credit during training (depreciation) in order to achieve the desired lifestyle. In the subsequent active working life, the income rises more and more and is then used to build up wealth (save) and to repay the loans. In the retirement phase, the income is lower again (pension receipt) and the saved assets are used (depreciation). At the end of life (at the optimal point in time of death), the wealth accumulated over a lifetime is completely used up, that is, saving and un-saving cancel each other out. This oversimplified model assumes that the individual has received no inheritances or gifts, and neither debts nor assets, during his lifetime.

The permanent income theory, on the other hand, predicts what income will be available to the consumer over his lifetime. The empirical relevance of the life cycle theory is very controversial. Some authors describe them as "extremely unrealistic", while the largely common practice of seniority pay (increasing pay according to occupation or age) supports the hypothesis.

Derivation

With respect to a consumer, the following is assumed:

• he still has T years to live
• his fortune amounts to the amount W
• he expects an income Y until the end of his life
• he works for another R years and then retires from working life

For the sake of simplicity, it is also assumed that the interest rate (and thus interest income from savings) is zero. The amount that is now available to the consumer results from his wealth W and his lifetime income ( R * Y ). The consumer can distribute this amount over the remaining years T of his life. The life cycle hypothesis now implies that the consumer smooths his consumption over this period T, i.e. divides the available amount in equal parts.

${\displaystyle {\mathit {C}}=(W+RY)/T\!}$

If you transform this equation, you get the following consumption function for the consumer:

${\displaystyle {\mathit {C}}=(1/T)W+(R/T)Y\!}$

The aggregated macroeconomic consumption function is then

${\displaystyle {\mathit {C}}=\alpha W+\beta Y\!}$

with the marginal propensity to consume from wealth α and the marginal propensity to consume from 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 maximizes his utility. The utility function has the usual neoclassical assumptions. It does not contain any inheritance motive. In simplified terms, the benefit of future periods is valued at the same time as the benefit of the current period (no subjective time discount). The individual has a constant income from work all his life ; in simple terms , retirement is not assumed. The property V earns the interest rate r . The calculation is then: Maximize the utility function

${\displaystyle \int \limits _{1}^{T}\mathrm {u(c_{t})} \,\mathrm {d} t}$

special

${\displaystyle \sum _{t=1}^{T}\ln(c_{t})}$

under the constraints

${\displaystyle {\mathit {c}}_{t}+s_{t}=e+rV_{t-1}\!}$ as a budget equation and

${\displaystyle {\mathit {V}}_{t}=V_{t-1}+s_{t}\!}$ as the stock equation of wealth as well

${\displaystyle {\mathit {V}}_{o}=0\!}$and as a start and end condition. ${\displaystyle {\mathit {V}}_{T}\geq 0\!}$

After creating the Lagrange approach , applying the Kuhn-Tucker conditions and the partial derivative according to and after calculating the consumption of each period, the result is the following savings function ${\displaystyle {\mathit {c}}_{t}\!}$ ${\displaystyle {\mathit {V}}_{T}\!}$

${\displaystyle {\mathit {s}}_{t}=(1+r)^{t-1}\left\lbrack e-{\frac {c_{1}(r,e)}{(1+r)}}(1+rt)\right\rbrack \!}$

That is normalized and discounted to the first period

${\displaystyle {\mathit {s}}_{t}=e-{\frac {c_{1}(r,e)}{(1+r)}}(1+rt)\!}$

${\displaystyle {\mathit {c}}_{1}(r,e)\!}$stands for the consumption of the first period and is a fixed number, depending on interest and income. The savings are discounted over the course of a lifetime. In this model, consumption increases at the rate of the capital market interest rate. Since is always greater than , the subtractor in the normalized equation becomes greater and greater over time, which reduces the savings. For high interest rates, one can initially see an increase in savings in the undiscounted model. But if you discount these values ​​down to the beginning of the life cycle calculation, these also become lower and lower. ${\displaystyle {\mathit {(}}1+rt)\!}$ ${\displaystyle {\mathit {(}}1+r)\!}$

Individual evidence

1. ↑ ^{a b c} Alisch: Wirtschaftslexikon. 16th edition. Gabler Verlag, Wiesbaden 2004.
2. ^ Mankiw: Macroeconomics. 4th edition. Schäffer-Poeschel, Stuttgart 2000, p. 597.
3. ↑ ^{a b} Dieckheuer: Macroeconomics - Theory and Politics. 4th edition. Springer, Berlin 2001, pp. 407-408.
4. ↑ Dornbusch / Fischer / Startz: Macroeconomics. 8th edition. Oldenbourg, Munich, Vienna 2003, p. 404.
5. ↑ ^{a b} Dornbusch / Fischer / Startz: Macroeconomics. 8th edition. Oldenbourg, Munich, Vienna 2003, pp. 403–404.
6. ↑ ^{a b} Feess / Tibitanzl: Macroeconomics. Volume 2. Franz Vahlen, Munich 1994, p. 60.
7. ^ Snowdon / Vane: An Encyclopedia of Macroeconomics. 1st edition. Elgar, Cheltenham 2002, pp. 488-489.
8. ^ Mankiw: Macroeconomics. 4th edition. Schäffer-Poeschel, Stuttgart 2000, p. 496.
9. ^ Snowdon / Vane: An Encyclopedia of Macroeconomics. 1st edition. Elgar, Cheltenham 2002, p. 488.
10. ^ William A. Jackson (1998): The Political Economy of Population Aging. Cheltenham, UK / Northampton MA, USA, p. 51.
11. ↑ Christian Christen (2011): Political Economy of Old Age Insurance. Marburg, p. 288.
12. ↑ ^{a b} Dornbusch / Fischer / Startz: Macroeconomics. 8th edition. Oldenbourg, Munich, Vienna 2003, p. 403.
13. ↑ ^{a b} Feess / Tibitanzl: Macroeconomics. Volume 2. Franz Vahlen, Munich 1994, p. 59.
14. ↑ Flaschel / Groh / Proaño: Keynesian Macroeconomics - Underemployment, Inflation and Growth. 2nd Edition. Springer, Heidelberg 2008, p. 163.
15. ^ Mankiw: Macroeconomics. 4th edition. Schäffer-Poeschel, Stuttgart 2000, p. 497.

bibliography

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