Permanent income hypothesis

A Model of the Permanent Income Hypothesis

A model of the Permanent Income Hypothesis

The permanent income hypothesis (often abbreviated PIH) is a model in the field of economics to explain the formation of consumption patterns. It suggests consumption patterns are formed from future expectations and consumption smoothing. The theory was developed by Milton Friedman and published in his A Theory of Consumption Function, published in 1957 and subsequently challenged by Robert Hall's inclusion of rational expectations. Originally applied to consumption and income, the process of future expectations is thought to influence other phenomena. In its simplest form, the hypothesis states changes in permanent income (human capital, property, assets), rather than changes in temporary income (unexpected income), are what drive changes in consumption.

Nobel laureate and inventor of the Permanent Income Hypothesis Milton Friedman

The formation of consumption patterns opposite to predictions was an outstanding problem faced by the Keynesian orthodoxy. Friedman's predictions of consumption smoothing, where people spread out transitory changes in income over time, departed from the traditional Keynesian emphasis on a higher marginal propensity to consume out of current income.

Income consists of a permanent (anticipated and planned) component and a transitory (unexpected and surprising) component. In the permanent income hypothesis model, the key determinant of consumption is an individual's lifetime income, not their current income. Unlike permanent income, transitory incomes are volatile.

Background and history

Until A Theory of Consumption Function, the Keynesian absolute income hypothesis and interpretation of the consumption function were the most advanced and sophisticated. In its post-war synthesis, the Keynesian perspective was responsible for pioneering many innovations in recession management, economic history, and macroeconomics. Like the neoclassical school that preceded it, early inconsistencies had their roots in socio-political events contrary to the predictions put forward.

The introduction of the absolute income hypothesis is often attributed to John Maynard Keynes, a British economist, who wrote several books which are now the basis for Keynesian economics. The hypothesis put forward by Keynes was accepted and placed into the post–war synthesis. However, inconsistencies were not resolved swiftly, and economists were unable to explain the consistency of the savings rate in the face of rising real incomes (Fig. 1).

Relationship between Saving and Consumption Based on Budget Data

United States (USD) Date Consumer Units Avg. Income APC MPC 1881–90 Selected wage-earner families $682 .90 .67 1901 Selected wage-earner normal families $651 .92 .68 1917–19 Selected wage-earner families $1,513 .91 .78 1935–36 Nonrelief nonfarm families $1,952 .89 .73 1935–36 Nonrelief farm families $1,259 .87 .57 1941 Urban families $2,865 .92 .79 1941 Farm families $1,680 .83 .57 1944 Urban families $3,411 .82 .57 1947 Urban families $3,323 .92 .78 1950 Nonfarm families $4,084 .91 .73 1950 Spending units of one or more persons $3,220 .92 .75 Fig. 1: Analysis of consumption and income; taken from Friedman (1957)

Before the neoclassical synthesis was established, Keynes and his hypothesis challenged the orthodoxy of neoclassical economics. As a result of the Great Depression, Keynes rapidly became among the leaders of economic thought. His MPC and MPS spending multipliers developed into the absolute income hypothesis (1), and were influential to the government responses to the ensuing depression.

$C=a+b\cdot Y_{d}$ (1)

Origins

The American economist Milton Friedman developed the permanent income hypothesis in his 1957 book A Theory of the Consumption Function. In his book, Friedman posits a theory that explained how and why future expectations change consumption.

Friedman's 1957 book created the basis for consumption smoothing. He argued the consumption model, in which outcomes are stochastic, where consumers face risks and uncertainty to their labor incomes, complicates interpretations of indifference curves, and causes consumers to spread out or 'smooth' their spending based off of their permanent income, which represents their anticipated income over their lifetimes. Friedman explain in A Theory of the Consumption Function how consumers interact with money based off of not just windfall gains, but through their permanent income because consumers will save when they expect their long term income to rise. He writes:

'Yet from another point of view, the assumption seems highly implausible. Will not a man who receives an unexpected windfall use at least some part of it in "riotous living," i.e. in consumption expenditures? Would he be likely to add the whole of it to his wealth? The answer to these questions depends greatly on how "consumption" is defined. The offhand affirmative answer reflects in large measure, I believe, an implicit definition of consumption in terms of purchases, including durable goods, rather than in terms of the value of services. If the latter definition is adopted, as seems highly desirable in applying the hypothesis to empirical data—though unfortunately I have been able to do so to only a limited extent—much that one classifies offhand as consumption is reclassified as savings. Is not the windfall likely to be used for the purchase of durable goods? Or, to put it differently, is not the timing of the replacement of durable goods and of additions to the stock of such goods likely to some extent to be adjusted so as to coincide with windfalls?'

— A Theory of Consumption Function

Theoretical considerations

In his theory, John Maynard Keynes supported economic policy makers by his argument emphasizing their capability of macroeconomic fine tuning. For Keynes, consumption expenditures are linked to disposable income by a parameter called the marginal propensity to consume (the amount per dollar consumers are willing to spend; $1-MPS=MPC$). Since the marginal propensity to consume itself is a function of income, it is also true that additional increases in disposable income lead to diminishing increases in consumption expenditures. It must be stressed that the relation characterized by substantial stability links current consumption expenditures to current disposable income—and, on these grounds, a considerable leeway is provided for aggregate demand stimulation, since a change in income immediately results in a multiplied shift in aggregate demand (this is the essence of the Keynesian case of the multiplier effect). The same is true of tax cut policies. According to the basic theory of Keynes, governments are always capable of countercyclical fine tuning of macroeconomic systems through demand management, although Friedman disputes this, arguing in a 1961 journal article that Keynesian macroeconomic fine tuning will succumb to 'long and variable lags.'

Model of the consumption function, where a is autonomous consumption, b is the MPC, and Yd is disposable income.

The permanent income hypothesis questions this ability of governments. However, it is also true that permanent income theory is concentrated mainly on long run dynamics and relations, while Keynes focused primarily on short run considerations. Friedman's argument, which challenged the use of fiscal policy in smoothing out business cycles, was challenged by stressing the relation between consumption and disposable income still follows (more or less) the mechanism supposed by Keynes.

Friedman starts elaborating his theory under the assumption of complete certainty. Under such circumstances, for Friedman, two motives exist for a consumer unit to spend more or less on consumption than its income: The first is to smooth its consumption expenditures through appropriate timing of borrowing and lending; and the second is either to realize interest earnings on deposits if the relevant rate of interest is positive, or to benefit from borrowing if the interest rate is negative.

According to the PIH, the distribution of consumption across consecutive periods is the result of an optimizing method by which each consumer tries to maximize his utility. At the same time, whatever ratio of income one devotes to consumption in each period, all these consumption expenditures are allocated in the course of an optimization process—that is, consumer units try to optimize not only across periods but within each period.

Calculation of income and consumption

Friedman's 1957 book also made an argument for an entirely new way of calculating income (income is represented by the variable $y$) by differentiating between transitory and permanent income (which was also taken to include ordinal elements like human capital and talents). In A Theory of Consumption Function, Friedman develops: $y=y_{p}+y_{t}$ as a formula. In an earlier study, Friedman, Kuznets (1945), he makes the case for a similar conception of income:

'The dichotomy between permanent and transitory components of a man's income, as was noted above, necessarily does violence to the facts. An accurate description of the factors determining a man's income must substitute a continuum for the dichotomy. This continuum is bounded at one extreme by "truly" permanent factors—those that affect a man's income throughout his career— and at the other by the "truly" transitory—those that affect his income only during a single time unit, where a time unit is the shortest period during which it seems desirable to measure income, in our case, a year, but conceivably a month, a week, a day, an hour, or even a minute. Between these extremes fall what may be called "quasi-permanent" factors, factors whose effects neither disappear at once nor last throughout a man's career. The quasi permanent factors can be ordered according to the length of time during which their effects persist: two-year factors, three-year factors, etc. A man's income can then be conceived as the sum of the parts attributable to each set of factors:

Income in any year =

permanent component

+ quasi-permanent component

+ transitory component.'

— Incomes from Independent Professional Practice

Friedman also developed a consumption formula, $c=c_{p}+c_{t}$, with $c_{p}$ meaning the permanent component of consumption, with $c_{t}$ being the transitory component. Friedman also drew a distinction between $y_{t}$ and $c_{t}$. Transitory consumption can be interpreted as surprising or unexpected bills, such as a high water bill, or unexpected doctor's visit, which, in Friedman's mind, cannot be spurred by $y_{t}$, because unexpected or 'surprise' consumption is not often financed through windfall gains.

Simple model

Consider a (potentially infinitely lived) consumer who maximizes his expected lifetime utility from the consumption of a stream of goods $c$ between periods $t$ and $T$, as determined by one period utility function $u(\cdot )$. In each period $t$, he receives an income $y_{t}$, which he can either spend on a consumption good $c_{t}$ or save in the form of an asset $A_{t}$ that pays a constant real interest rate $r$ in the next period.

The utility of consumption in future periods is discounted at the rate $\beta \in (0,1)$. Finally, let $\operatorname {E} _{t}[\cdot ]$ denote expectation conditional on the information available in period $t$. Formally, the consumer's problem is then

$\max _{\{c_{k}\}_{k=t}^{T}}\operatorname {E} _{t}\sum _{k=0}^{T-t}\beta ^{k}u(c_{t+k})$

subject to

$A_{t+1}=(1+r)(A_{t}+y_{t}-c_{t}).$

Assuming the utility function is quadratic, and that $(1+r)\beta =1$, the optimal consumption choice of the consumer is governed by the Euler equation

$c_{t}=\operatorname {E} _{t}[c_{t+1}].$

Given a finite time horizon of length $T-t$, we set $A_{T+1}=0$ with the understanding the consumer spends all his wealth by the end of the last period. Solving the consumer's budget constraint forward to the last period, we determine the consumption function is given by

$c_{t}={\frac {r}{(1+r)-(1+r)^{-(T-t)}}}\left[A_{t}+\sum _{k=0}^{T-t}\left({\frac {1}{1+r}}\right)^{k}\operatorname {E} _{t}[y_{t+k}]\right].$ (2)

Over an infinite time horizon, we instead impose a no Ponzi game condition, which prevents the consumer from continuously borrowing and rolling over his debt to future periods, by requiring

$\lim _{t\to \infty }\left({\frac {1}{1+r}}\right)^{t}A_{t}=0.$

The resulting consumption function is then

$c_{t}={\frac {r}{1+r}}\left[A_{t}+\sum _{k=0}^{\infty }\left({\frac {1}{1+r}}\right)^{k}\operatorname {E} _{t}[y_{t+k}]\right].$ (3)

Both expressions (2) and (3) capture the essence of the permanent income hypothesis: current consumption is determined by a combination of current non human wealth $A_{t}$ and human capital wealth $y_{t}$. The fraction of total wealth consumed today further depends on the interest rate $r$ and the length of the time horizon over which the consumer is optimizing.

Liquidity constraints

Some have attempted to improve Friedman's original hypothesis by including liquidity constraints, most notably Christopher D. Carroll.

Empirical evidence

Observations, recorded from 1888 to 1941, of stagnant average propensity to consume in the face of rising real incomes provide strong evidence for the existence of the permanent income hypothesis. An early test of the permanent income hypothesis was reported by Robert Hall in 1978, and, assuming rational expectations, finds consumption follows a martingale sequence. Hall & Mishkin (1982) analyze data from 2,000 households and find consumption responds much more strongly to permanent than to transitory movements of income, and reinforce the compatibility of the PIH with 80% of households in the sample. Ben Bernanke (1984) finds 'no evidence against the permanent income hypothesis' when looking at data on automobile consumption.

Median American household spending

In contrast, Flavin (1981) finds consumption is very sensitive to transitory income shocks ('excess sensitivity'), while Mankiw & Shapiro (1985) dispute these findings, arguing that Flavin's test specification (which assumes income is stationary) is biased towards finding excess sensitivity.

Souleles (1999) uses income tax refunds to test the PIH. Since a refund depends on income in the previous year, it is predictable income and should thus not alter consumption in the year of its receipt. The evidence finds that consumption is sensitive to the income refund, with a marginal propensity to consume between 35 and 60%. Stephens (2003) finds the consumption patterns of social security recipients in the United States is not well explained by the permanent income hypothesis.

Stafford (1974) argues that Friedman's explanation cannot account for market failures such as liquidity constraints. Carroll (1997) and Carroll (2001) dispute this, and adjust the model for limits on borrowing. A comprehensive analysis of 3000 tests of the hypothesis provides another explanation. It argues that rejections of the hypothesis are based off publication bias and that after correction, it is consistent with data.

Policy implications

Unresolved inconsistencies explain the failure of transitory Keynesian demand management techniques to achieve its policy targets. In a simple Keynesian framework the marginal propensity to consume (MPC) is assumed constant, and so temporary tax cuts can have a large stimulating effect on demand. The PIH framework suggests that a consumer will spread out the gains from a temporary tax cut over a long temporal horizon, and so the stimulus effect will be much smaller. The permanent income hypothesis has evidence supporting such a view, such as Shapiro & Slemrod (2003).

Criticism

Liquidity constraints

Some critics of the permanent income hypothesis, such as Frank Stafford, have criticized the permanent income hypothesis for its lack of liquidity constraints. However, some studies have adapted the hypothesis for certain circumstances and found that the permanent income hypothesis is compatible with liquidity constraints and other market failures unaccounted for in the original hypothesis.

Income inequality

There is some evidence that affluent households tend to save more than poorer households. Alvarez-Cuadrado & Van Long (2011) find this evidence contrary to the major tenets of the permanent income hypothesis.

Praise

File:MFriedmanNobel.jpg

Friedman received the 1976 Sveriges Riksbank prize in Economic Sciences in Memory of Alfred Nobel 'For his achievements in the field of consumption analysis, monetary history and theory and for his demonstration of the complexity of stabilization policy.' The 'consumption analysis' has been interpreted by Worek (2010) as representing Friedman's contributions in the form of the permanent income hypothesis, while the monetary history and stabilization section has been interpreted to refer to his work on monetary policy and history, and monetarism, which seeks to stabilize a currency, preventing erratic swings, respectively.

Austrian School

The Permanent Income Hypothesis has been met with praise from Austrian economists.

See also

• Consumption smoothing
• Income#Economic definitions
• Milton Friedman
• Ricardian equivalence
• Risk compensation
• Milton Friedman bibliography

References

• Friedman, Milton (1957). A Theory of Consumption Function. Princeton University Press. ISBN 0-691-04182-2.
• Meghir, Konstantinos (2004). "A Retrospective on Friedman's Theory of Permanent Income". The Economic Journal. 114 (496). Oxford University Press: 293–306. JSTOR 3590064 – via JSTOR.
• Friedman, Milton; Kuznets, Simon (1945). Incomes from Independent Professional Practice. National Bureau of Economic Research. ISBN 0-87014-044-2.
• Carlin, Wendy; Soskice, David (2014). Macroeconomics: Institutions, Instability, and the Financial System. Oxford University Press. ISBN 9780199655793.
• Carroll, Christopher D. (2001). "A Theory of the Consumption Function, with and without Liquidity Constraints". The Journal of Economic Perspectives. 15 (3). American Economic Association: 23–45. JSTOR 2696555 – via JSTOR.
• Keynes, John Maynard (1936). The General Theory of Employment, Interest and Money. The United Kingdom: Palgrave Macmillan. ISBN 978-0-230-00476-4.
• Friedman, Milton (1961). "The Lag in Effect of Monetary Policy". Journal of Political Economy. 69 (5). University of Chicago Press: 447–466. JSTOR 1828534 – via JSTOR.
• Keynes, John Maynard (1923). A Tract on Monetary Reform. Pickle Partners Publishing. ISBN 1789120713.
• Ireland, Peter N. (1995). "Using the Permanent Income Hypothesis for Forecasting". FRB Richmond Economic Quarterly. 81 (1): 49–63. SSRN 2129374 – via SSRN.
• Carroll, Christopher D. (1997). "Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis". The Quarterly Journal of Economics. 112 (1): 1–55. doi:10.1162/003355397555109.
• Hall, Robert E. (1978). "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence". Journal of Political Economy. 86 (6). University of Chicago Press: 971–987. doi:10.1086/260724.
• Hall, Robert E.; Mishkin, Frederic S. (1982). "The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households". Econometrica. 50 (2): 461–482. doi:10.2307/1912638. JSTOR 1912638 – via JSTOR.
• Bernanke, Ben S. (1984). "Permanent Income, Liquidity, and Expenditure on Automobiles: Evidence From Panel Data" (PDF). The Quarterly Journal of Economics. 99 (3): 587–614. JSTOR 1885966 – via JSTOR.
• Flavin, Marjorie A. (1981). "The Adjustment of Consumption to Changing Expectations About Future Income". Journal of Political Economy. 89 (5). University of Chicago Press: 974–1009. doi:10.1086/261016.
• Mankiw, N. Gregory; Shapiro, Matthew D. (1984). "Trends, Random Walks, and Tests of the Permanent Income Hypothesis". Journal of Monetary Economics. 89 (5): 165–174. doi:10.1016/0304-3932(85)90028-5.
• Souleles, Nicholas S. (1999). "The Response of Household Consumption to Income Tax Refunds". American Economic Review. 89 (4): 947–58. doi:10.1257/aer.89.4.947.
• Stephens, Melvin (2003). "'3rd of tha Month': Do Social Security Recipients Smooth Consumption Between Checks?" (PDF). American Economic Review. 93 (1): 406–422. doi:10.1257/000282803321455386.
• Stafford, Frank P. (1974). "Permanent income, wealth, and consumption: A critique of the permanent income theory, the life cycle hypothesis, and related theories". Econometrics. 2 (2). Berkeley: University of California Press: 195–196. doi:10.1016/0304-4076(74)90040-2. hdl:2027.42/22322. ISSN 0304-4076 – via Elsevier Science Direct.
• Runkle, David E. (1991). "Liquidity constraints and the permanent-income hypothesis: Evidence from panel data". Journal of Monetary Economics. 27 (1). Elsevier: 73–98. doi:10.1016/0304-3932(91)90005-9. ISSN 0304-3932 – via Elsevier Science Direct.
• Havranek, Tomas; Sokolova, Anna (2020). "Do consumers really follow a rule of thumb? Three thousand estimates from 144 studies say 'probably not'". Review of Economic Dynamics. 35. Elsevier: 97–122. doi:10.1016/j.red.2019.05.004. ISSN 1094-2025 – via Elsevier Science Direct.
• Lee, Tong Hun (1975). "More on Windfall Income and Consumption". Journal of Political Economy. 83 (2). University of Chicago Press: 407–417. JSTOR 1830930 – via JSTOR.
• Shapiro, Matthew D.; Slemrod, Joel (2003). "Consumer Response to Tax Rebates". American Economic Review. 93 (1). National Bureau of Economic Research: 381–396. CiteSeerX 10.1.1.159.3723. doi:10.1257/000282803321455368.
• Alvarez-Cuadrado, Francisco; Van Long, Ngo (2011). "The Relative Income Hypothesis". Journal of Economic Dynamics and Control. 35 (9): 1489–1501. ISSN 0165-1889 – via Elsevier Science Direct.
• Worek, Michael (2010). Nobel: A Century of Prize Winners. Buffalo, New York: Firefly Books. ISBN 978-1-55407-780-9.
• Block, Walter E. (2013). "Was Milton Friedman a Socialist? Yes". MEST Journal. 1 (1): 11–26. doi:10.12709/MEST.01.01.01.02.PDF.
• Mulligan, Robert F. (2014). "The Central Fallacy of Keynesian Economics". Quarterly Journal of Austrian Economics. 17 (3). Mises Institute: 338–364. ISSN 1936-4806.
• Thomas, R. Leighton (1985). Introductory Econometrics, Theory and Applications. London: Longman. ISBN 058229634X. OCLC 10348689.
• Forder, James; Monnery, Hugo (2019). "Why Did Milton Friedman Win the Nobel Prize? A Consideration of His Early Work on Stabilization Policy". Economic Journal Watch. 16 (1). Fraser Institute: 130–145.
• Mankiw, N. Gregory (2006). "The Macroeconomist as Scientist and Engineer". Journal of Economic Perspectives. 20 (4): 29–46. CiteSeerX 10.1.1.214.5101. doi:10.1257/jep.20.4.29.
• Stirzaker, David (2005). Stochastic Processes and Models. Oxford University Press. ISBN 9780198568148.
• Mankiw, Gregory N.; Taylor, Timothy (2006). Principles of Microeconomics. ISBN 978-0324319163.