Previous research on consumption has suggested that lagged income is a good predictor of current consumption and also assumed that income was an endogenous variable in the consumption function. Hall’s paper disagrees with this hypothesis and instead proposes we consider income to be an exogenous function and that apart from trend, marginal utility obeys a random walk. Hall finds that when consumers act in a rational way, it is evident that the conditional expectation of future marginal utility is a function of today’s level of consumption alone, with all other information being irrelevant.
Consumers process all available information each period about current and future earnings, also taking into account financial assets accumulated from past earnings, to determine an appropriate level of consumption. This finding suggests that lagged income should have no predictive power with respect to consumption.
Taking a quadratic form, Hall’s theoretical work is based on the assumption that consumers face a known, constant, real interest-rate. If the real interest rate varies over time in a way that is known with certainty, the results would remain true with certain amendments, specifically lambda would vary as a response. In the presence of a guaranteed rate there is no need for precautionary saving among consumers, making the model not entirely realistic.
Hall uses the functional form: u(ct)=1/2(c¯-ct)^2
This is used to test his theoretical hypothesis. This forms his utility function as a result. As such, this explains that utility must be maximised as consumers process the choices of their current consumptions or future consumptions thereby easily deducing the correct optimal marginal utility.
Additionally, Hall implements F-tests for variable exclusions. This is done using lagged income, and then lagged wealth, lagging indicators. If lag in the underlying structural consumption function is non-optimal, then lagged income will have more predictive power for current consumption beyond that of lagged consumption and as such the life-cycle-permanent income hypothesis would be rejected.
As such, the hypothesis assumes to have a form of estimating conditional expectation: E(ct|ct-1,xt-1), p1=lambda and p2=0, this shows that disposable income and consumption follow a stochastic process, where xt-1 is a vector of data in period t-1.
The data Hall used to test his hypothesis was a quarterly estimate of consumption of non-durables and services from 1948-77 in 1972 US dollars, divided by population, collated by the US National Income and Product Accounts. He also uses the market value of corporate stocks as a proxy for wealth.
Since it is widely accepted that wealth has a strong influence on consumption, Hall decides to test the impact of lagged wealth, with the prediction that wealth in earlier quarters should have no predictive power with respect to this quarter’s consumption. Stock market prices conveniently provide reliable quarterly data which Hall uses to test this hypothesis.
He finds the F-statistic for the hypothesis that the coefficients of lagged stock prices are all zero to be 6.5, greater than the critical value of 2.4 at 5% significance. Further, each coefficient tested individually is different from zero according to the standard t-test. Compared to equation 1.3, this regression has a smaller standard error of about 20 cents (from $14.6 to $14.4).
This leads to the conclusion that the Permanent Income Hypothesis is rejected by the data. The stock market does have some value in predicting consumption one quarter into the future.
For the policy maker, Hall’s research finds that policy affects consumption only as much as it affects permanent income. This is based on the fact that any information available today about future income is already incorporated in people’s expectations of their permanent income. Therefore, only new information about taxes and other policy instruments can affect permanent income. This means that the policy analyst is faced with the difficult task of estimating the effect of a proposed policy change on permanent income, in order to predict its effect on consumption.
Increasing long term consumption through transitory policies (such as tax cuts) is not possible. Individuals must believe the changes are permanent to alter their consumption.