Hall looks at the life cycle-permanent income hypothesis.Hall describes his findings of two problems with the conventional life-cycle permanent income hypothesis: in cases where transitory income changes consumption is not always able to follow its optimal path, liquidity and other constraints prevent it. Secondly if the consumption function is not related to the optimal distributed lag then additional predictive powers will be present beyond simply lagged consumption, possibly lagged income or wealth.
The data reveals real disposable income contains no additional predicting power for consumption, however the index of stock prices, acting as lagged wealth, did. Hall’s findings support the need for life-cycle permanent income hypothesis to be modified so that it recognises this lagged relationship between wealth (measured by an index of stock prices) and consumption.
He finds in the table 1 data that the ‘predictive value of lagged marginal utility for current marginal utility is extremely high’, in fact it’s explained by over 99.5% through the model for all three equations (1.0, 1.2, 1.3). This reinforces the widespread belief that past actual consumption is a useful tool for forecasting future consumption. The F-test conducted on equation 1.3 (from table 1) with extra lagged periods found that periods beyond one period of lagged consumption are insignificant at the 5 percent level. The approach to use only last period’s consumption and none further back is therefore a reasonable approach in simplifying the analysis. Table 3 tested the relevance of real disposable income on the consumption function and found insignificant predictive power to be added (reinforcing the statement made earlier). Hall also finds in the table 1 data that his assumption of ϒ≈1 is supported with the output of the three equations all off by less than .02. This supports his conclusion that consumption takes the form of a random walk with a trend as marginal utility is rather constant.
Hall contends the marginal utility of consumption, assuming that the interest rate is similar to the rate of time preference, has a random walk but tends to trend upwards, obeying the regression relation \(u'(c_{t+1}) = \gamma u'(c_t) + \epsilon _{t+1}\) where \(\gamma = (1+\delta)/(1+r)\) and \(\epsilon_{t+1}\)
If the utility function is quadratic then the regression obeys \(c_{t+1} = β_0 + \gamma c_t - \epsilon_{t+1}\)
If the utility function has a constant elasticity of substitution form the changes in consumption is described by \(c_{(t+1)}^{(-1/σ)} = ϒc_t^{(-1/σ)}+ ϵ_{t+1}\)
Hall believes that the results of Ordinary Least Squares will be unbiased, so it has a good function form.
F tests for variable exclusion are used. Essentially, he tests to see if introducing additional data other than past consumption allows the model to have more predictive power. This is done using lagged income, and then lagged wealth, as regressors.
For example lagged income is tested by setting \(E(c_t | c_{t-1},y_{t-1},y_{t-2}) = \lambda c_{t-1} + μ(\rho_1 - \lambda) y_{t-1} + μ\rho_2y_{t-2}\) Reject life cycle-permanent income hypothesis unless \(\rho_1 = \lambda\) and \(\rho_2 = 0\), which means disposable income and consumption follow an identical stochastic process, and therefore permanent income and observed income are the same thing, confirming the hypothesis.
Data on consumption of nondurables and services in 1972USD sourced from the United States National Income and Product Accounts from 1948 - 1977. When testing for wealth impacts, stock prices acts as the variable for wealth.
The impact of lagged wealth changes on consumption is statistically significant with an F-statistic of 6.5, but numerically small none-the-less. With last year’s stock price having a positive impact on consumption of 22% with a 5% standard error.
The pure life cycle-permanent income hypothesis states that present consumption cannot be influenced by any lagged variable is rejected.
As consumption matters for fiscal policy, both in terms of aggregate demand and taxation through GST, government can use lagged data to assist with forecasts and impacts of policy.
Consumption should be forecast with past consumption treated as an exogenous variable, lagged wealth can also assist governments to forecast consumption and take policy action if necessary and such addition would improve their accuracy.