Robert E. Hall - ‘Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence’

Describe Hall’s findings.

Hall finds that the time-series data he used implies that we should reject the ‘pure life cycle-permanent income hypothesis’, that consumption in some period, \(c_{t}\), can’t be predicted by any variable dated \(t - 1\) or earlier other than \(c_{t-1}\). His tests indiciate that change in stock prices in the immediately preceding quarter have some, albeit quite small, predictive power.

However, he suggests that a slight modification of the hypothesis - a caveat that some part of consumption takes time to adjust to a change in permanent income - means that it is compatible with this finding, and therefore the important implications that the theory has for fiscal policy still remain true.

What assumption does Hall make about the utility function? Is this a good choice in functional form?

With the assumption of a known, constant real interest rate, as well as the assumption that utility is concave (i.e. has diminishing returns), and the assumption that people choose consumption to maximise their expected lifetime utility in light of all information available at that time, Hall is able to construct the following function:

\(E_{t}u'(c_{t+1}) = [(1 + \delta) / (1 + r)]u'(c_{t})\)

where \(u\) is a strictly concave utility function, \(c_{t}\) is consumption, \(\delta\) is the rate of subjective time preference, and \(r\) is the real interest rate.

This function has the following implications:

No information available in period \(t\) apart from the level of consumption, \(c_{t}\) helps predict future consumption
Marginal utility obeys the regression relation, \(u'(c_{t+1}) = (1 + \delta) / (1 + r)u'(c_{t}) + \epsilon_{t+1}\)
Consumption itself obeys a random walk, apart from trend.
If the utility function has the quadractic form, \(u(c_{t}) = -\frac{1}{2} (\bar{c}-c_{t})^2\), where \(\bar{c}\) is the bliss level of consumption,

then consumption obeys the exact regression, \(c_{t+1} = \beta_{0} + \gamma c_{t} - \epsilon_{t+1}\), where \(\beta_{0} = \bar{c}(r-\delta)/(1+r)\)

If the utility function has the CES form, \(u(c_{t}) = c_{t}^{\sigma-1/\sigma}\) then the regression will be \(c_{t+1}^{-1/\sigma} = \gamma c_{t}^{-1/\sigma} + \epsilon_{t+1}\)

The quadratic utility function is particularly helpful in that its derivation is simply \(u' = \bar{c}-c_{t}\). It is also consistent with the reasonable assumption of diminishing returns. Hall confirms that using this functional form is appropriate by comparing regressions of consumption on its own lagged value using both the quadratic form and the CES form. He finds that there is a negligible difference.

How does Hall turn his theory into a testable hypothesis?

Hall turns the theory into a testable hypothesis by estimating the conditional expectation, \(E(c_{t}|c_{t-1}, x_{t-1})\), where \(x_{t-1}\) is a vector of data known in period \(t-1\). That is, he estimates the effect of both past consumption and some other variable on current consumption. He can then test if the variable, \(x\) has a statistically significant effect on current consumption.

What data does he use to test the hypothesis?

He uses quarterly data on the consumption of nondurables and services in 1972 dollars from the U.S National Income and Product Accounts, divided by the population.

By dropping durables altogether, he says he is able to avoid the suspicion that the findings are affected by the possibly dubious procedure used for imputing a service flow to the stock of durables.

What does he find to be the impact of lagged wealth changes on consumption? Is this consistent with the Permanent Income Hypothesis?

He uses stock prices as a measure of wealth and finds that lagged changes in stock prices have a statistically significant impact on consumption.

As stated earlier, this is inconsistent with the ‘pure’ Permanent Income Hypothesis, but it is consistent with a slightly modified version of the hypothesis.

What are the implications for fiscal policy?

Halls suggests that based on the results of his paper, consumption should be treated as an exogenous variable, beyond the next few quarters, in line with the general spirit (i.e. Hall’s modified version) of PIH. This is, of course, not in line with the conventional Keynesian view that consumption is influenced by changes in contemporaneous income, rather than changes in permanent income only.

If Hall’s findings are to be trusted, then analysis of fiscal policy must not consider contemporaneous changes in income to have an effect on consumption. Policies that aim to have some effect on consumption, such as stabilisation policy, must be designed to impact what a person believes their permanent income to be, since policies that merely have a transitory impact on income do not have a transitory impact on consumption.

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