Therefore when regression 2 is estimated by ols do

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Therefore, when regression (2) is estimated by OLS, do not forget to multiply the value of the estimated slope coefficient by 0.01, or, what amounts to the same thing, divide it by 100. If you do not keep this in mind, your interpretation in an application will be highly misleading . For example, if in an application one finds that 1 = 300, the absolute change in Y is (0.01)(300) = 3 (See Appendix 1 for interpretation issue). C. Reciprocal Models Models of the following type are known as reciprocal models . 0 1 1 t t t Y u X (3) which may also be expressed as follows: 0 1 t t t Y Z u where 1 t t Z X . Here, note that 1 1 2 2 1 .( ) t t t t t t t t dY dY dZ dX dZ dX X X  , hence it is not constant.
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ECON 301 - Introduction to Econometrics I April, 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 19 Example TC=FC+VC(Q)= 0 1 t X . Then 0 1 1 t t ATC u X . Below you can find a summary for the functional forms in terms of slope and elasticity relationships. Table Functional Forms: Slope and Elasticities Appendix 1 Interpretation of Semi-log Models Note hat the relative in t Y is given by: t t-1 t t-1 Y Y relative in Y Y . Hence, if t Y has increased from 100 to 130, t relative in Y is 0.30. On the other hand, the percentage in t Y is given by: t t-1 t t-1 . Y Y percentage in Y 100 Y
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ECON 301 - Introduction to Econometrics I April, 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 20 Hence, if t Y has increased from 100 to 130, t percentage in Y is 30%. (1) Suppose that you are given the following estimated log-lin model: ln 2 0.2 t t Y X Here, t 1 t relative in Y 0.2 absolute in X implies that: 1 t unit in X (causes) 0.2 relative t in Y or 1 t unit Δ in X (causes) 20 percent t Δ in Y Hence, the estimated model says that: 1 unit change in t X will lead to 20% change in t Y . (2) Suppose that you are given the following estimated lin-log model: ˆ 12 0.6ln t t Y X Here, t 1 t absolute in Y 0.6 relative in X implies that: 1 t relative in X (causes) 0.6 unit t in Y or 100 t percent in X (causes) 0.6 unit t in Y or, simply ; 1 t percent Δ in X (causes) 0.006 unit t Δ in Y Hence, the estimated model says that: 1 % change in t X will lead to 0.006 unit change in t Y .
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