This week’s homework is based on Robert Hall’s 1978 paper “Stochastic implications of the Life Cycle-Permanent Income Hypothesis: Theory and evidence”, available here: http://web.stanford.edu/~rehall/Stochastic-JPE-Dec-1978.pdf.
Give it a good read or two. There will be a few new concepts in the paper.
• Euler equation (Euler was Swiss, so we pronounce his name “Oyler”). The Euler equation is one that can help to characterise the equilibrium of a dynamic optimisation problem. It relates the key variables in the model over time along their utility-maximising path.
• Random walk. This is a series whose changes cannot be predicted, other than with a trend. While all random walk series have a unit root, not all unit root series are a random walk. (why?)
• F-test. This is a method of testing whether a simpler model does a better job of explaining the data than a more complex model that contains all the variables in the simple model and some more.
Halls basic point was that consumption is unpredictable. That is disposable income barely carries any predictive power because current income cannot necessarily predict future consumption. Previous to his paper, the prevailing thought in economics was that past incomes influenced people’s view about their permanent income and thus determined present consumption. That is a permanent change in income will determine one’s current consumption levels; people change their consumption habits based on the future. Consumers basically outlook their future consumption and consume in the present based on those estimates. A policy such as a permanent decrease in tax rate would hence increase current consumption. Hall theorized that the relationship between current consumption levels and the expected future income. This also implied that without a drastic change in future income, current consumption will not significantly change.
Hall assumes the utility function to be quadratic and that the Euler Equation directs an agent’s optimal consumption choice. Consumption follows a random walk if we assume a time preference rate to be close or on par with the real interest rate.
Robert Hall noted that the marginal utility obeys a random walk i.e. consumer consumption level is highly random and there is no correlation in-between current consumption level and future consumption level. This was due to exogenous factors that might influence individual level of consumption which also include purchasing trend. In his word, when consumer maximizes expected further utility, it is shown that the conditional expectation of future marginal utility is a function of today’s level of consumption alone. It is a bad choice in functional form. The strong stochastic implication of the life cycle-permanent income hypothesis is that only consumption lagged one period should have a non-zero coefficient in such a regression.
In order to test the theory, Hall apply the life cycle-permanent income hypothesis for the application of the theory of the consume to the problem of dividing consumption between the past and future. The hypothesis suggest that consumer estimate their ability to consume in the long run and set current consumption to the appropriate fraction of that estimate
He uses data from earlier time periods in hypothesis that consumption is unrelated to any economic variables. He tests if lagged income values have any potential to explain consumption. Next he tests consumption explanatory power of the lagged wealth by observing historic stock data.
Halls uses per capita levels by gathering data from United States National Income and Product Accounts dividing it by the population. Hall uses the USD and with 1972 as the base year. Consumption data used are non-durables and services.
Hall writes that through the use of stock exchange data that it did make a somewhat of a prediction of future consumption. Hall refers to it as the lagged wealth changes. He claims that this however is minor. This is inconsistent with the permanent income hypothesis. Lagged variables are rejected in permanent income hypothesis as past consumption determines current consumption.
The paper transformed the way macroeconomist think of consumption and its unpredictability. An impact of this on fiscal policy could be the question of whether non-permanent incentives for consumption (i.e. short term tax reductions or subsidies) fuel current consumption. It could be argued that aggregate consumer demand cannot be manipulated by short-term incentives. Drastic changes to permanent income must be seen by consumers for them to change their consumption habits.