ECON301_Handout_09_1213_02

Below you can find a summary for the functional forms

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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 YY 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 . 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 tt YX  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 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 .
ECON 301 - Introduction to Econometrics I April, 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 21 Appendix 2 How to Measure the Growth rate: Use of Log-Lin Model Economists, businesspeople, and governments are often interested in finding out the rate of growth of certain economic variables, such as population, GNP, money supply, employment, productivity, and trade deficit. You may recall the following well-known compound interest formula, in discrete form, from your introductory course in economics. 5 (A2.1) t 0 Y Y (1 ) t r  where r is the compound (i.e., over time) rate of growth of Y . Taking the natural logarithm of (A2.1) produces: (A2.2) t 0 lnY lnY ln(1 ) tr Letting 00 and 1 ) r , model becomes: t 01 lnY t  Adding the disturbance terms we get the following log-lin model, 5 The continuous form is t0 YY rt e .

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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 22 (A2.3) t 01 lnY t tu  where the independent variable (regressor) is “time,” which will take values of 1, 2, 3, etc. The coefficient of the trend variable in the growth model (A2.3), 1 , gives the instantaneous (at a point in time) rate of growth 6 and not the compound (over a period of time) rate of growth. But the latter can be easily found from 1 ln(1 ) r  as 1 1 re  .
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