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Unformatted text preview: e unit of measurement of
the dVar and eVars change? Melissa Tartari (Yale) Econometrics 42 / 93 Algebraic Properties: Unit of Measurement I
How do the OLS estimates change when the unit of measurement of
the dVar and eVars change?
They do so in an entirely expected way! Melissa Tartari (Yale) Econometrics 42 / 93 Algebraic Properties: Unit of Measurement I
How do the OLS estimates change when the unit of measurement of
the dVar and eVars change?
They do so in an entirely expected way! Consider (2.9) yi = βo + β1 xi + ui , and notice that changing the unit
of yi is like multiplying it by some constant number c , call the new
dVar yi0 = cyi . Melissa Tartari (Yale) Econometrics 42 / 93 Algebraic Properties: Unit of Measurement I
How do the OLS estimates change when the unit of measurement of
the dVar and eVars change?
They do so in an entirely expected way! Consider (2.9) yi = βo + β1 xi + ui , and notice that changing the unit
of yi is like multiplying it by some constant number c , call the new
dVar yi0 = cyi .
Multiply each side of (2.9) by c
cyi = c βo + c β1 xi + cui
or equivalently
0
0
yi0 = βo + β1 xi + ui0 Melissa Tartari (Yale) where Econometrics 0
0
βo = c βo & β1 = c β1 42 / 93 Algebraic Properties: Unit of Measurement I
How do the OLS estimates change when the unit of measurement of
the dVar and eVars change?
They do so in an entirely expected way! Consider (2.9) yi = βo + β1 xi + ui , and notice that changing the unit
of yi is like multiplying it by some constant number c , call the new
dVar yi0 = cyi .
Multiply each side of (2.9) by c
cyi = c βo + c β1 xi + cui
or equivalently
0
0
0
0
yi0 = βo + β1 xi + ui0
where
βo = c βo & β1 = c β1
ˆˆ
Recall that βo , β1 where the estimates obtained when regressing yi
ˆ0 ˆ0
on xi . Thus, if we regress y 0 on xi we obtain estimates β , β s.t.
i ˆ0
βo
Melissa Tartari (Yale) o ˆ
= c βo &
Econometrics ˆ0
β1 1 ˆ
= c β1
42 / 93 Algebraic Properties: Unit of Measurement II What happe...
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This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.
 Fall '10
 DonaldBrown
 Econometrics

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