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## intersect, setdiff, setequal, union## Warning: package 'latex2exp' was built under R version 3.2.2What is cointegration? Why should consumption and income be cointegrated? Why should stock prices and dividends be cointegrated? Cointegration refers to a relationship between two time series datasets which at least one follows a random walk, but the respective paths of the variables are correlated. A stable relationship can be established between the two variables over time and deviations in this relationship can be used to determine the nature of shocks.
Consumption and income should be cointegrated because while consumption follows a random walk, according to the Permanent Income Model it maintains a stable relationship with income over time. Individuals adjust their consumption with respect to income when they believe there will be a permanent shift in income. In practical terms, this makes sense. If we believe we will have more expendable income for the foreseeable future, we may be more likely to spend it. Whereas, if we believe the increase will only be temporary, we are likely to save the income which will not greatly affect our permanent income and use it to make up for unforeseen shortfalls or expenses.
The paper argues that stocks and dividends have a similar relationship to GDP and consumption, in that in the same way that consumption responds to shocks in GDP, dividends will respond to shocks. Furthermore, dividends, like consumption follow a random walk. Following this, it seems appropriate to cointegrate the dividend and stock prices, to reflect their relationship.
What is the point of the paper? The paper aims to determine the transitory components of a shock to GNP and stock prices, using a two variable autoregression. Cochrane contends that shocks to stock prices and GNP are almost completely transitory. This indicates that when consumption is constant, a shock to GNP will be mostly transitory. As well as this, when dividends are constant, a shock to share prices will also be mostly transitory.
What do you make of an increase in stock prices without a corresponding increase in dividends? Is it likely to be permanent or transitory? Why? An increase in stock prices without a corresponding increase in dividends is likely to be transitory, given that it negatively impacts the expectated future returns.
What do you make of a drop in GDP that is accompanied by a fall in consumption? Is it likely to be a permanent or transitory shock? If a drop in GDP is accompanied by a fall in consumption, it is likely that the drop has been a permanent shock. Following the Permanent Income Model, individuals will only change their consumption if they believe the shock is permanent. The paper notes that this model is not perfect and can be rejected through statistical analysis, however, the papers suggests that Permanent Income model functions approximates the relationship well enough to appropriately interpret the data.
What does Cochrane mean by saying that consumption defines the trend in GDP? The paper argues that GNP and consumption are cointegrated and consequently, their long run relationship remains stable. This stable relationship comprises a ratio of consumption to GNP, where consumption follows a nearly random walk. As consumption obeys a random walk, it is GNP that must adjust to reestablish the long term stable ratio when the two variables deviate from this.