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Unformatted text preview: I378 JOURNAL OF POLITICAL ECONOMY A First Lesson in Econometrics Every budding econometrician must learn early that it is never in good
taste to express the sum of two quantities in the form: 1+1=2. (1) Any graduate student of economics is aware that
l = 1n e, (2)
and further that
1 = sian + coszq. (3) In addition, it is obvious to the casual reader that m 1
= 7. (4)
1120 2
Therefore equation (1) can be rewritten more scientiﬁcally as
. (5? 1
2 2 _ __
ln e + (sm q + cos q) — "2:40 2” (5) It is readily conﬁrmed that 1 = cosh p \/1 — tanth, (6)
and since
1 (5
e=lim(1+—)a (7)
6am 8 equation (5) can be further simpliﬁed to read: 6
1n[lim (l + 713)] + (sinzq + cos2 q)
(54m
00 cosh V1 — tanth
=2 —p——2——— (8)
11:0
If we note that
0! = 1, (9) The work on this paper was supported by no one. The author would like to credit
an unknown but astute source for the original seeds for the analysis. MISCELLANY 1379 and recall that the inverse of the transpose is the transpose of the inverse, we can unburden ourselves of the restriction to onedimensional space by
introducing the vector X, where (X')‘1 — (X'1)' = 0 (10)
Combining equation (9) with equation (10) gives
[(X’)‘1 — (X‘1)'l! = 1, (11) which, when inserted into equation (8) reduces our expression to In lim {[(X’f1 — (X‘1)’] + %}} + (sian + cos2 q) 6400
00 ﬂ
2 20 cosh p\/1 2n tanh p_ (12) At this point it should be obvious that equation (12) is much clearer and
more easily understood than equation (1). Other methods of a similar
nature could be used to simplify equation (1), but these will become
obvious once the young econometrician grasps the underlying principles. JOHN J. SIEGFRIED
University of Wisconsin ...
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 Three '11
 ProJim
 Econometrics

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