1. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
In the years after the Second World War, econometricians working with macroeconomic data were puzzled by the fact that the long-run average propensity to consume seemed to be roughly constant despite the marginal propensity to consume being much lower. 1

2. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
A model in which current consumption was just a function of current income could not explain this phenomenon and was therefore clearly too simplistic. 2

3. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
Several more sophisticated models were developed which could explain this apparent contradiction, one of them being Friedman's Permanent Income Hypothesis. 3

4. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
According to the Permanent Income Hypothesis, permanent consumption, CP, is proportional to permanent income, YP. Permanent income is a subjective notion of likely medium-run future income. Permanent consumption is a similar notion of consumption. 4

5. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
Actual consumption, C, and actual income, Y, consist of these permanent components plus unanticipated transitory components, CT and YT, respectively. 5

6. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
It is assumed, at least as a first approximation, that the transitory components of consumption and income have expected value 0 and are distributed independently of their permanent counterparts and of each other. 6

7. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
To solve the problem that permanent income is unobservable, Friedman hypothesized that it is subject to an adaptive expectations process, permanent income at time t being updated by a proportion of the difference between actual income and permanent income at time t –1. 7

8. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
Hence permanent income at time t is a weighted average of actual income at time t and permanent income at time t –1. 8

9. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
This relationship can be used to substitute for permanent income in the relationship between permanent consumption and permanent income. We have also substituted for permanent consumption using the identity for actual consumption. 9

10. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
Thus we obtain current consumption as a function of current income and permanent income lagged one period. 10

11. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
The latter is unobservable, but it can be eliminated by lagging the adaptive expectations process and substituting. Of course, we still have an unobservable variable, permanent income lagged two periods, on the right side of the equation. 11

12. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
After lagging and substituting s times, we obtain the equation shown. It is reasonable to assume that l lies between 0 and 1, and so (1 – l) will also lie between 0 and 1. (1 – l)s will therefore be a declining function of s, and for s large enough the final term can be dropped. 12

13. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
The specification is nonlinear in parameters and Friedman fitted it using an appropriate nonlinear estimation method. 13

14. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
Alternatively, the model may be represented in ADL(1,0) form. This could be done using the manipulation shown at the end of the adaptive expectations sequence. 14

15. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
An equivalent procedure is to take the expression for Ct, lag it by one time period, and multiply through by (1 – l). 15

16. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
We subtract this expression from the previous one and all the terms cancel, except the first one and the disturbance terms.. 16

17. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
Hence we obtain an expression for Ct in terms of Yt, Ct–1, and a compound disturbance term. 17

18. ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS
The short-run marginal propensity to consume is given by the coefficient of Yt, b2l, and the long-run propensity is b2. Since l is less than 1, the model is able to reconcile a low short-run marginal propensity to consume with a higher long-run average propensity. 18

19. Copyright Christopher Dougherty 2013.
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