Is the Permanent Income Hypothesis Glass Half Full ?

This is one of my usual boring posts on the same things I often type about. I have nothing much new to say and certainly won’t present any new evidence.

There is no good reason to click “more.” In case anyone hasn’t guessed my answer, it is that I know of no good reason to be confident that the permanent income hypothesis is even partially true to any useful extent.

To begin at the beginning, the Permanent Income Hypothesis is the conjecture that it is useful to model consumption savings choices by treating consumption at different times as consumption of different goods and imagining an agent who maximizes an inter-temporal utility function subject to an inter temporal budget constraint. I add that I think of it as including the assumption that it is useful to model aggregate consumption as the decisions of a representative consumer. The PIH as introduced by Friedman did not include the assumption that the consumer has rational expectations and thus did not imply that the resulting choices were optimal. However current usage of the phrase now implies, at least, that the assumption of rational expectations is a good approximation.

So far even with a representative consumer with rational expectations, there isn’t enough there to justify the word hypothesis. That is to say the assumptions have no implications at all without some further assumptions about the utility function. The key standard assumption which gives content to the PIH is that utility is the sum of pleasure from consumption and a function of everything else we care about (that the utility function is additively separable in consumption and everything else). This is a very standard assumption in main stream macroeconomics. It is often relaxed if the aim is to test the PIH and to avoid rejecting it (yes I am asserting that this research program starts from the conclusion). But, as far as I know, the assumption is almost always made and used when the PIH is used (rather than protected from the data).

These assumptions are enough to get a falsifiable hypothesis as is demonstrated by the fact that the PIH with separability is rejected by the data. Predictable changes in income should not be associated with changes in consumption and they are. The typical macroeconomist’s reaction (as always) is to shrug his or her shoulders and say that models are false by definition and the Permanent Income Model (PIM) is useful, because it captures some aspects of the data, that is provides explanations for some otherwise puzzling patterns.

My way of putting this is to consider the PIH an alternative hypothesis to the Keynesian null that intertemporal budget constraints can be neglected when modeling aggregate consumption.

The glass half empty and half full conjecture is that both the PIH and the Keynesian hypothesis are rejected by the data.

By when I say Keynesian hypothesis I use “Keynesian” in the sense of “Keynes’s” as in

(6) Changes in expectations of the relation between the present and the future level of income. — We must catalogue this factor for the sake of formal completeness. But, whilst it may affect considerably a particular individual’s propensity to consume, it is likely to average out for the community as a whole. Moreover, it is a matter about which there is, as a rule, too much uncertainty for it to exert much influence.

Note the crucial point that Keynes conjectured that expectations of future income have a negligible effect on aggregate consumption. This is important since it means that the clear evidence that individual consumption depends on predictable changes in individual income is perfectly consistent with Keynes’s hypothesis.

Ignoring what Keynes wrote, many economists have been convinced that the PIH has something useful to add to Keynes based on individual data. There are many ways in which households with low future expectable income for a given current income have low consumption for a given current income (one is that for the same income African Americans consume less that white Americans). This isn’t evidence against Keynes, but it seems that it could be considered evidence against vulgar-Keynes who forgot Keynes’s qualification. In any case it is basically universally considered proof that the PIH glass is half full (e.g. by Paul Krugman).

This reasoning is invalid. The reason (explained by Steve Marglin decades ago) is that all of the cross section patterns can be just as well explained as ways in which households with low past income for a given current income have low consumption for a given current income. This pattern can be explained if consumption is addictive (habit formation) or if one has to learn how to spend income. It is now very widely agreed that aggregate consumption can’t be explained without the assumption of habit formation. Consumption doesn’t fluctuate as much as predicted by simple models without habit formation (that is models with utility functions which are additively separable over time as well as over consumption and everything else). So the part about forecasting future income approximately rationally is not needed to fit the patterns. In fact it adds nothing useful.

I can think of a few ways to test the Keynesian null that the PIM adds nothing useful. To get a testable null, it is necessary to replace Keynes’s English with an equation. Given that there are 5 other factors listed (in that chapter) and another chapter on consumption, this is a bit of a challenge. I for one (and who cares) would be satisfied with an equation giving consumption as a function of current and lagged incoome, current wealth and lagged consumption. The null is that consumption is not related to future income once those variables are included.

1) The obvious way to try to test this is to instrument future income and use the fitted values as expected income in a two stage regression. This will not work, because there really aren’t instruments which are correlated with future income but which we can be confident don’t affect consumption directly.

2) theory gives a good hint as to a test. The PIH implies Ricardian equivalence. The argument is that the timing of taxes doesn’t matter, because the state has a budget constraint and forward looking consumers understand that they (or their heirs) will have to pay for government spending sooner or later. Here the evidence is not kind to the PIH. I know of solid evidence that tax cuts cause increased consumption. I don’t know of solid evidence that they have a smaller effect than they would if consumers considered them a windfall with no implications for future taxes.

3) Time trends. There are persistent differences in growth rates across countries. People in China should be quite confident that future income will be higher compared to current income for them than for people in the USA. There is also a clear pattern relating growth rates and savings rates. The ratio of consumption to current income is low in countries for which the ratio of future income to current income is high. Ah the wrong sign. The data correspond to habit formation and myopia. This doesn’t amount to much (or anything really) and doesn’t influence anyone’s opinion (even mine).

4) information about future income in consumption. This is getting somewhere. If agents forecast future income and if agents have information we don’t supply to the computer, then consumption should be useful in forecasting future income. In fact it does add information which isn’t there in current income and a few lags of income. This observation (due to Cochrane IIRC) is indeed evidence that there is something to the PIM. However it is only a rejection of the Keynesian null if the forecasts of income which don’t use data on consumption are as good as they can be without using data on consumption. When GDP is low compared to a moving average of past GDP, it typically grows quickly (the weasel word “typically” is needed really only for 1931, 1932, 1937 and the past few years). With habit formation and myopia (and in the data) consumption is well fit using a geometric moving average of lagged disposable income.

Another way of putting it is that in recessions the ratio of consumption to GDP is high and the mean of future GDP growth is high. It is easy to explain the first fact with habit formation. It is easy to use the second fact to forecast GDP a bit better than with a low order auto-regression.

I’m not convinced that there is anything there. I am also not convinced there is nothing there. I should be running regressions in which future GDP growth is regressed on consumption and a moving average of lagged income not typing this.

5) survey elicited expectations. There are surveys in which people are asked to forecast future GDP or more generally to say if they expect economic conditions to improve. This may have nothing to do with rational expectations, but such survey expectations should help explain consumption in models which already include disposable income (and lags) wealth and lagged consumption. I am shamefully ignorant of this literature, but I don’t know of much evidence of this.

I’m not sure that Keynes’s null has been convincingly rejected. This may just be due to my ignorance.

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