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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**ADAPTIVE EXPECTATIONS: FRIEDMAN'S PERMANENT INCOME HYPOTHESIS**

The specification is nonlinear in parameters and Friedman fitted it using an appropriate nonlinear estimation method. 13

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**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

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**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

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**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

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**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

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**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

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**Copyright Christopher Dougherty 2013.**

These slideshows may be downloaded by anyone, anywhere for personal use. Subject to respect for copyright and, where appropriate, attribution, they may be used as a resource for teaching an econometrics course. There is no need to refer to the author. The content of this slideshow comes from Section 11.4 of C. Dougherty, Introduction to Econometrics, fourth edition 2011, Oxford University Press. Additional (free) resources for both students and instructors may be downloaded from the OUP Online Resource Centre Individuals studying econometrics on their own who feel that they might benefit from participation in a formal course should consider the London School of Economics summer school course EC212 Introduction to Econometrics or the University of London International Programmes distance learning course 20 Elements of Econometrics

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