By Jack Johnston, John DiNardo

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**Extra info for Econometric Methods, Fourth Edition**

**Example text**

Snce varl-kn) declines monotonically with incresing n. there exists a number n. k ' . ia - 1 I #. < e) > 1 - is then said te converge lim Prlp in probability to the constant p.. 23) - 6J = . 24) ln words, the probability of kn lying in an arbitrarily small intcrval about g can be' made as close to unity as we desire by letting n become sufhcicntly large. A qiu-hsnd way of writing 1. 25) Jt = vn where plim is an abbreviaon of probability Iimit. The sample mean is then said to be a consistent estimator of g.

For example, if the origin is set at mid-1935 and the unit of measurementis 1 year, then the year 1942 corresponds to t 7, and so forth for the other years. lf the origin is set at end-1940 (beginningof 1941) and the unit Show that any of measurement is 6 rqpnths, then 1937 corresponds to t value + choice of origin and unit bt is unaffecte,d by the trend Xt computed a nis = -7. = = of measurement. (c) Let ert and eyt denote the residuals of X and F from their trend values. Calculate the correlation coefficient between ert and eyt.

Cixi = satished y. cixi and vartl7'l . *l an d so 2N wftcf 37 Fltcj varty) + c2 = wj)2 - as given in te text, which proves the theorem. 5 To derive vartec) From Eq. ) co = - uo I'i - Square both sides and take expectations. The expectations of a1lthree cross-product terms vanish. 3 above tat E E(: /)i11 0. 1. How might the volatility of the savings and income series in Fig. 1J be measured? A possible measure is the coefficient of variation, which is the standard deviation of a series expressed as a percentage of the mean.