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Lecture 18 Cointegration

RS EC2 - Lecture 1811 Lecture 18 Cointegration Suppose ytand xtare I(1). We regress ytagainst xt. What happens? The usual t-tests on regression coefficients can show statistically significant coefficients, even if in reality it is not so. This the spurious regression problem(Granger and Newbold (1974)). In a Spurious Regression the errors would be correlated and the standard t-statisticwill be wrongly calculated because the variance of the errors is not consistently : This problem can also appear with I(0) series see, Granger, Hyung and Jeon (1998). Spurious Regression RS EC2 - Lecture 182 Examples:(1) Egyptian infant mortality rate (Y), 1971-1990, annual data, on Gross aggregate income of American farmers (I) and Total Honduran money supply (M) = - .2952 I - .0439 M, R2= .918, DW = .4752, F = ( ) ( ) ( ) Corr = .8858, , (2). US Export Index (Y), 1960-1990, annual data, on Australian males life expectancy (X) = -2943. + X, R2= .916, DW =.

RS – EC2 - Lecture 18 5 •An mx1 vector time series Yt is said to be cointegrated of order (d,b), CI(d,b) where 0<b d, if each of its component series Yit is I(d) but some linear combination ’Yt is I(d b) for some constant vector ≠0. • : cointegrating vector or long-run parameter. • The cointegrating vector is not unique. For any scalar c

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