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Life-cycle hypothesis

By Craig Wright | 19 Jun 2017 | Bitcoin & Blockchain Tech

The life-cycle hypothesis is a relatively simple model based on a micro-economic analysis of family spending habits that was developed by Franco Modigliani and Richard Brumberg (1954) in the early 1950’s. It sure has many similarities with Friedman’s (1957) model of income expenditure. The primary assumptions of each model start with an assumption that consumers seek to maximise the utility they obtain through both their current and future consumption habits. In each theory, it is assumed that the only effects that will influence current assumption are associated with long-term income changes. In each model, temporary fluctuations in income level would be saved or invested rather than being consumed.

This model contradicts the opinion expressed by Keynes (1937) that put forth an argument that “a greater proportion of income being saved as real income increases”. In Friedman’s model, the consumer plans over an infinite of time, this assumption is made through the inclusion of planning for one’s descendants. Modigliani took the alternative approach of limiting a consumer’s expenditure in planning period to be limited to their individual lifespans. This model incorporates a belief that a consumer saves to secure the consumption across their retirement age. Many economists use the income hypothesis (Friedman, 1957) and the life-cycle hypothesis (Modigliani & Brumberg, 1954) interchangeably.

The theoretical basis of the Life Cycle Hypothesis of consumption

Franco Modigliani and Richard Brumberg proposed a theory of spending (Modigliani and Brumberg, 1954) that used the concept of a utility function from an individual consumer that is based on rational decisions concerning the amount of expected income that the consumer will have and the amount that they can spend at each age. The only limit on this spending model was the limit of the resources that are available at each stage of the individual’s life. They extended this idea to incorporate the idea that the consumer maximises utility at each period subject only to the level of current income, discounted future income and current net worth (Ando and Modigliani, 1963).

This model was predicated on the assumption of rational expectation (Muth, 1961). Following the criticisms of Keynes’ consumption function (Keynes, 1937), researchers including Kuznets (1952) and Goldsmith (1955) conducted an econometric analysis of these early models. These early results appeared to refute Keynes’s work and have led to the development of many of the mainstay theories surrounding the life-cycle model of consumer spending. The life-cycle model does not require that there is any rigorous relationship between consumption and income in any short run period. Consequently, as Modigliani’s theory incorporates the individual’s expected lifespan as the planning unit for an individual’s consumption, the theory has come to be known as “life-cycle hypothesis” (LCH).

Modigliani relies on two primary assumptions that are central to the hypothesis:

1 Each individual plans to consume the income added even right throughout the lifetime;

2 The individual utility function that is created by the consumer forms I proportion of the resources that that individual plans to consume in any given period of their life. This consumption is determined only by the consumer’s preferences and not by the resources managed at any point.

Development of the Life-Cycle Hypothesis

Consumption has been the cornerstone of macroeconomics throughout the last century. Researchers such as Mitchell (1913) started using a theory of cyclic expansion to explain under-consumption within the United States. It was with Keynes where this was developed into a systematic study relating to nations macroeconomic performance to consumption. In “The General Theory of Employment, Interest and Money” (Keynes, 1937, Page 90), Keynes uses a simple equation to demonstrate how expenditure on consumption can be determined:

Life-cycle Hypothesis

(1)

In Equation (1) represents consumption and models income. To define the form of this function, Keynes argues, “men are disposed to increase their consumption when their income increases, but not by as much as the increase in their income” (Keynes, 1937, Page 96). From this, the derivative forms a constant that is referred to as the marginal propensity to consume. The predominant influencers to the propensity to consume are categorised to the objective factors and the subjective factors. Here objective factors include but are not restricted to:

· Movements in price level,

· Variations in the worth of capital, and

· Fluctuations around the interest rate.

Subjective factors cover the “animal spirits” as motives to consume and incorporate pleasure, generosity and indulgence. In this model, apart from variations in the prices, all other factors normally don’t alter the marginal propensity to consume (taken over short run periods). Hence, Keynes argues that once the price is removed as a factor, the level of consumption is predominantly contingent on income level.

Later economists (Modigliani, 1944; Duesenberry, 1949) have introduced modifications to Keynes’s original equation. In Equation (2) we see an early relationship between consumption and linear income where represents the marginal propensity to consume and is the coefficient of Y.

Life-cycle Hypothesis

(2)

In this model the relationship between consumption and income is linear. This is argued as consumers must spend to consume on life’s necessities just to ensure subsistence and thus this model is said to work even if individuals have no income.

A more recent and more complex version, known as the two-period consumption model is represented in Equation (3).

Life-cycle Hypothesis

(3)

In this, Keynes’ consumption function is extended to incorporate two variables:

· Labour Income:

Life-cycle Hypothesis

· Property Income:

Life-cycle Hypothesis

Ando and Modigliani (1963) made an argument that property income is a function of the high-income consumers and that these individuals have a lower propensity to consume. The result is that (the coefficient of) would correctly be smaller than (the coefficient of).

Modigliani and Brumberg further extended the two-factor consumption model to flatten consumption patterns over an individual’s lifetime in a manner that is independent of current levels of income.

Then construct an equation that relates current consumption with its determining factors:

Life-cycle Hypothesis

(4)

In Equation (4), current consumption is a linear, homogeneous function of current income, expected average income and preliminary assets. The coefficients depend on the age of the consumer (Modigliani & Brumberg, 1954). The variables and coefficients are defined as:

· represents an individual’s current consumption,

· and Y^e relate to existing and expected income,

· L represents the life span of an individual consumer,

· N represents that consumer’s length of time used in earning, and

· represents one’s assets at the beginning of the time-period.

Per Equation (4), current income effects current consumption only to a trivial degree. As the consumer over their remaining life span must evenly distribute income, it remains that a minor portion of any change in current income is all that will be allocated towards current consumption. Ando and Modigliani (1963) developed this theory to incorporate an aggregate consumption function for the life-cycle hypothesis. The result they obtained is substantially the same as Equation (4).

In the LCH, it is possible for a consumer’s expenditure to exceed income. This will occur through the making of major investments (the purchase of a family home) and investments in human capital (university studies) and is common early in an individuals’ life. AT this stage, the individual is said to be borrowing against their future. In this model, middle life is generally associated with increases in income and savings/investment. During this stage in life, the consumer repays loans and starts a savings fund for retirement. The last phase is associated with retirement, and in this stage, the consumer reduces expenditure and dis-saves until death.

It is argued that an individual will be more or less inclined to borrow against their future early in life dependent on their expected levels of wealth later in life. This is a function of the individual’s anticipated skills, talents, and initiative and is related directly to the degree to which an individual believes that they can later repay those debts and to how much they discount later activity (time preferences). An individual who does not believe in their future ability to earn would express higher rates of time preference which comes with a greater discounting of future activity.

Is the LCH viable given econometric data?

The LCH sees consumers storing and expending assets across different periods of their life. The consumer makes provision for retirement and modifies the consumption pattern throughout their life and at different ages independent to the income received at each age. This is a simple theory that can be developed into economy-wide predictions of consumer behaviour. The LCH leads to a further hypothesis that national savings are dependent upon the growth rate of the national income and not its level at any point in time. It further predicts that the aggregate wealth of the entire economy is related to the length of time that consumers throughout the economy spend within retirement.

The predictions posited using the LCH were unable to be tested in the 1950’s but have received Later empirical support (Modigliani,1966). More recent econometric methods allowed researchers to test these theories more rigorously. Keynes’ consumption function (1937) was generally accepted early on. With the increased ability to test the validity of economic theories started to become possible using time-series data, evidence started to be uncovered that conflicted with the theory. In the General Theory, Keynes claims:

“The fundamental psychological law, upon which we are entitled to depend with great confidence both a priori from our knowledge of human nature and from the detailed facts of experience, is that men are disposed, as a rule and on the average, to increase their consumption as their income increases, but not by as much as the increase in their income.” (Keynes, 1937, Page 96)

As such, with a rise in the level of income, the ratio between saving and income was predicted to increase correspondingly. Kuznets (1952) analysed saving patterns using data from the United States over the period 1899 to 1949. This study reported no significant increase in the ratio of savings. This was noted even as the levels of real income was demonstrated to increase significantly during this same period. Goldsmith (1955) confirmed these results.

The United States

Studies connected to the life-cycle hypothesis have been conducted by many economists and are becoming more commonplace as the creation of econometric tools as allowed for more robust testing methods. Robert Hall (1978) claims that empirical research focusing on the consumption function fails to address the endogenous distributions of income. Accordingly, the allocation of income into the consumption function as an independent variable would distort the estimated function to a significant degree. Hall (1978) offers a different method where he treats consumption as a random walk, this is expressed in Equation (5):

Life-cycle Hypothesis

(5)

Equation (5) resolves the problematic aspects of endogeneity, the problem is that this may offer little in explanatory power. Equation (5) states that present consumer spending is disparate to all other economic variables that are associated with any prior previous period. From this, the current consumption (and a random error) is all that would be required to predict future consumption.

From Hall’s analysis, he presents the result that “the pure life cycle hypothesis… is rejected by the data”.

Doubts concerning the rationality of consumer behaviour have been further voiced following the 2008 financial crisis. Cynamon and Fazzari (2008) present a model of consumption and financial behaviour that holds consistently both prior to and during the financial crisis. Their model offers an alternative description of consumer behaviour to the LCH.

Cynamon and Fazzari’s (2008) theory of consumption and financial behaviours delivers a more logically reliable account of behaviour when tested against the data using modern econometric methods and tools than does the LCH.

Various works that are critical of basic concepts of the life-cycle model include Campbell and Mankiw (1989), Palley (2002) and Setterfield (2010). The above-noted work of Cynamon and Fazzari theory (2008) that extends Duesenberry’s (1949) model of relative consumption also demonstrates flaws in the LCH. In this work, regression results indicate that some balance sheet variables are significant in the consumption function, even though they are not expected to be so under the life-cycle framework. Modigliani’s Life Cycle hypothesis fails to explain the data when exposed to econometric time-series models.

Japan
David Horlacher (2002) notes that:

“If the LCH is valid, then evidence should reveal an inverse relationship between the elderly dependency ratio and the household saving rate. Studies by Horioka based both on cross-sectional and time series evidence have confirmed that there is such an inverse relationship”.

He proceeds to present evidence that the elderly do dis-save. The problem here comes from findings () that demonstrate the elderly don’t dis-save as quickly as the model predicts. As Dekle (1990) reports, “the Japanese are keeping their wealth intact”, a result that does not accord with the LCH.

One rational purpose for this disparity is reported by Bernheim, Shleifer and Summers (1985). This is that most families seek to leave a bequest and aid their children, a particularly strong motive in Japan even if Horlacher (2002) dismisses it.

Conclusion and criticisms

Given that the life-cycle hypothesis describes the long run behaviour of consumers, a short run testing model is insufficient. OLS can only be used in an analysis of the short-term models. The models of both Friedman and Modigliani are based on long term effects and many earlier tests based on the use of OLS alone may be inadequate. Many models based on the use of applying OLS to macroeconomic data may lead to spurious results.

Palley (2002) reported that by the start of the 2000’s, the average debt-income ratio of households with income under USD $50,000 [1] was 298%. This alone demonstrates errors in the assumption of rational planning in the LCH. In the 2008 financial crisis, the long-term ability to maintain household debt growth was further discredited with household liabilities starting to drop abruptly.

We conclude that these variances in consumer debt are not explained through the models developed by Modigliani and Brumberg (1954). Consumer expenditure in the United States and Japan seem to be explained more effectively using models such as Campbell & Manikiw’s (1989) “explanation of “Rule of Thumb” consumers that long-term rational planners.

Many researchers (Fuhrer, 1992; Mayer, 1973; Mulligan, 2014) have empirically demonstrated that the estimates suggest that, in the short run (at least), consumers will respond more vigorously to a temporary policy change than the LCH would predict (Fuhrer, 1992).

The LCH obscures the relationship between current consumption and current income. Ando and Modigliani (1963) propose that the analysis of the association of current consumption to the present value of the whole future income for a consumer advocates that an alteration in current income not attended by an alteration in the planned future income would lead to a relatively minor alteration in the existing spending behaviour of a consumer. Individuals do not and could not be seen to have all the information that they require to make a complex calculation of their upcoming income decades into the future. The assumptions of spending patterns are likewise unrealistic.

No definite vision of life-time income, credit rates over one’s life, family structure, opportunities, etc. could be viably imagined by any individual no matter how rational they are.

References

1. Asteriou, D and Hall, S. G. (2007). Applied Econometrics. Palgrave Macmillan: New York, N.Y.

2. Ando, A. and Modigliani, F. (1963). The “Life Cycle” Hypothesis of Saving: Aggregate implications and Tests. American Economic Review, Vol. 53, №1, Part 1(Mar 1963), pp. 55–84.

3. Bernheim, D. B., Shleifer, A., Summers, L. (1985)The Strategic Bequest Motive, Journal of Political Economy

4. Campbell, J. Y. and Mankiw, G. (1989). Consumption, Income and Interest Rates: Reinterpreting the Time-Series Evidence. NBER Macroeconomic Annual.

5. Cynamon, B. Z. and Fazzari, S. M. (2008). Household Debt in the Consumer Age: Source of Growth — Risk of Collapse. Capitalism and Society, 3, 2, Article 3.

6. Dekle, R. (1990) Do the Japanese Elderly Reduce Their Total Wealth? A New Look with Different Data, Journal of the Japanese and International Economies

7. Duesenberry, J. S. (1949). Income, Saving and the Theory of Consumer Behavior. Massachusetts: Harvard University Press.

8. Friedman, M. (1957). A Theory of the Consumption Function. New Jersey: Princeton University Press.

9. Fuhrer, J. C., (1992), Do consumers behave as the life-cycle/permanent-income theory of consumption predicts? Federal Reserve Bank of Boston New England Economic Review (Sept./Oct. 1992), pp. 3–14 USA

10. Goldsmith, R. W. (1955). A Study of Saving in the United States. New Jersey: Princeton University Press.

11. Hall, R. E. (1978). Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence. Journal of Political Economy. 86:971–87. October 1978.

12. Horlacher,D. E., (2002) ‘Aging in Japan: Causes and Consequences’, Part II: ‘Economic Issues’

13. Keynes, J. M. (1937). The General Theory of Employment, Interest and Money. New York: Harcourt, Brace and Company.

14. Kuznets, S. (1952). Proportion of Capital Formation to National Product. American Economic Review, Vol. 16, pp. 507–526.

15. Mayer, T.,(1973) Permanent income, wealth, and consumption: A critique of the permanent income theory, the life cycle hypothesis, and related theories, (University of California Press, Berkeley)

16. Miles D., Scott A., Breedon F., (2012). Macroeconomics: Understanding the Global Economy, Publisher: John Wiley & Sons Incorporated

17. Mitchell, W. C. (1913). Business Cycles. Berkeley, University of California Press

18. Modigliani, F. and Brumberg, R. (1954) Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data. Post-Keynesian Economics.

19. Modigliani, F. (1944). Liquidity Preference and the Theory of Interest and Money. Econometrica. 1 (12): 45–88.

20. Modigliani, F. (1966). The Life Cycle Hypothesis of Saving, the Demand for Wealth and the Supply of Capital. Social Research. 33 (2): 160–217.

21. Mulligan, R. F., (2014) The Central Fallacy of Keynesian Economics Quarterly Journal of Austrian Economics (11/19/2014)

22. Muth, J. F., (1961) “Rational Expectations and the Theory of Price Movements, reprinted in The new classical macroeconomics. Volume 1. (1992): 3–23 (International Library of Critical Writings in Economics, vol. 19. Aldershot, UK: Elgar.)

23. Palley, I. T. (2002). Economic contradictions coming home to roost? Does the U.S. economy face a long-term aggregate demand generation problem? Journal of Post Keynesian Economics, Fall 2002, Vol. 25, №1 9.

24. Setterfield, M. (2010). Real Wages, Aggregate Demand and the Macroeconomic Travails of the U.S. Economy: Diagnosis and Prognosis. Trinity College Department of Economics Working Paper, 10–05.

[1] At the time, this accounted for 66.2% of the total US population.