rec09 - MIT OpenCourseWare http:/ocw.mit.edu 14.384 Time...

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MIT OpenCourseWare http://ocw.mit.edu 14.384 Time Series Analysis Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Consumption, Income, Wealth and Cointegration 1 14.384 Time Series Analysis, Fall 2008 Recitation by Paul Schrimpf Supplementary to lectures given by Anna Mikusheva October 31, 2008 Recitation 9 Consumption, Income, Wealth and Cointegration There is a long line of papers that use cointegration to examine the relationship among consumption, income, and wealth. These notes go over two such papers, one relatively old and one more recent. Campbell (1987): Does Saving Anticipate Declining Labor Income? An Al- ternative Test of the Permanent Income Hypothesis Briefly, the permanent income hypothesis says that consumption should only change in response to changes in expected lifetime income, or “permanent income.” Since permanent income is unobservable, the permanent ± ² ² income hypothesis (PIH) cannot be tested directly. Hall (1978) observed that under rational expectations, the PIH implies that consumption should be a martingale ( E [ c t +1 |I t ] = c t 1 ). Many authors have implemented tests based on this fact, such as Mankiw and Shapiro (1985) as mentioned in lecture 16. Tests based on this fact generally reject the PIH. Campbell develops an alternative test, both to con±rm Hall’s result and to better understand how the PIH fails. Model Let y kt and y lt denote capital and labor income at time t , c t denote consumption, W t wealth, and r the interest rate. The PIH model maintains that y kt = rW t . Let’s also allow from some unforecastable capital gains, η t . Then the evolution of wealth is W t = (1 + r ) W t 1 + y l,t 1 c t 1 + η t We can rewrite the budget
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rec09 - MIT OpenCourseWare http:/ocw.mit.edu 14.384 Time...

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