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Monday 16 January 2012

The permanent income hypothesis


The permanent income hypothesis
The permanent income hypothesis (PIH) is a theory of consumption that was developed by the American economist Milton Friedman. In its simplest form, the hypothesis states that the choices made by consumers regarding their consumption patterns are determined not by current income but by their longer-term income expectations. The key conclusion of this theory is that transitory, short-term changes in income have little effect on consumer spending behaviour.
Measured income and measured consumption contain a permanent (anticipated and planned) element and a transitory (windfall gain/unexpected) element. Friedman concluded that the individual will consume a constant proportion of his/her permanent income; and that low income earners have a higher propensity to consume; and high income earners have a higher transitory element to their income and a lower than average propensity to consume.
In Friedman's permanent income hypothesis model, the key determinant of consumption is an individual's real wealth, not his current real disposable income. Permanent income is determined by a consumer's assets; both physical (shares, bonds, property) and human (education and experience). These influence the consumer's ability to earn income. The consumer can then make an estimation of anticipated lifetime income.
Transitory income is the difference between the measured income and the permanent income. It can be calculated simply by subtracting the measured income and the permanent income.
There is a corollary to the permanent income hypothesis named the permanent production hypothesis. This hypothesis stipulates that the choices made by producers regarding their production patterns are determined not by their present term capital cost but by their longer-term capital cost expectations. The key conclusion of this theory is that transitory, short term changes in capital costs have little effect on production behaviour.
The idea behind the permanent-income hypothesis is that consumption depends on what people expect to earn over a considerable period of time. As in the life-cycle hypothesis, people smooth out fluctuations in income so that they save during periods of unusually high income and disserve during periods of unusually low income. Thus, a pre-med student should have a higher level of consumption than a graduate student in history if both have the same current income. The pre-med student looks ahead to a much higher future income, and consumes accordingly.

Early Keynesian models of the consumption function related current consumption expenditure to current levels of income or disposable income. These models took the form of:
C = a + bYd
where
C = Consumption Expenditure
a = Autonomous consumption
consumption expenditure independent of the level of income.
b = the Marginal Propensity to Consume 'MPC'
which represents the fraction of each additional dollar of income 
devoted to consumption expenditure.
and
Yd = Current Disposable Income. 
Several theoretical implications can be developed by taking the ratio of consumption expenditure to the level of disposable income. This ratio known as the 'APC' the average propensity to consume eliminates the need to convert nominal values into their real counterpart in that changes in the price level cancel out:
APC = Real Consumption
                   Real Income
= Nominal Consumption / P =   Nominal Consumption
      Nominal Income/P                 Nominal Income 
Thus the APC can be computed by dividing both sides the the Keynesian consumption function by disposable income: 
   APC = C/Yd = a/Yd + b (Yd/Yd)
Or
APC = a/Yd + MPC. 
Given this final result we can look at the theoretical implications of the Keynesian consumption function over a different income groups (the cross- section) and over time (a time series). For the cross-section we would expect that lower-income groups would consume a greater proportion of their income relative to high-income groups: 
APC low income > APC high income 
With time series data we would expect that over time and as disposable income increases the APC should decline:
APCt-1 > APC > APCt+1
It is in this latter case that this particular consumption function fails to explain real world behaviour. In empirical studies, the APC is observed to be smaller for higher income groups relative to low income groups. However, over time the APC is observed to be constant independent of growth in aggregate measures of income. This failure led to the development of alternative theories of the consumption function one of which is the Permanent Income Hypothesis or 'PIH'.
The PIH begins to explain consumption behaviour by first redefining measures of income. Observed values of aggregate income 'Y' can be divided up into two separate components: 'YP' Permanent (or projected levels of) Income and 'YT ' Transitory (or unexpected changes in) Income. Thus:
Y = YP + YT.
The transitory component has an expected value of zero (E [YT t] = 0) reflecting the notion that over time transitory gains are offset by future transitory losses and vice-versa.  Thus in the long run observed levels of income 'Y' are equal to permanent income 'YP'.
Finally, according to the PIH consumption expenditure is proportional to permanent income:
C = kYP such that the parameter 'k', a constant, represents both the average propensity to consume and the marginal propensity to consume. This consumption function (as shown with the blue line below) is described more accurately as a long run consumption function consistent with the observed long run results of consumption behaviour. 
Observed short run behaviour is explained through the value of transitory income for different income groups. Specifically, transitory income for low income groups is assumed to be negative reflecting the notion that over time transitory losses exceed transitory gains for this group of individuals:
  YTL < 0 => YL < YPL
For middle income groups the value of transitory income is equal to zero over time such that observed and permanent income takes the same value:
   YTM = 0 => YM = YP
Finally, for high income groups, transitory gains exceed transitory losses such that transitory income is on average positive over time or: 
  YTH > 0 => YH > YP
The impact of this transitory component can be used to develop a short run consumption function (the red line) as shown in the diagram.