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Unformatted text preview: 2.4 Units of Measurement and Functional FormTwo important econometric issues are: 1) Changing measurementWhen does scaling variables have an effect on OLS estimates?When does scaling variables have no effect on OLS estimates? 2) Functional FormsHow do natural logs affect linear regressions?How do functional forms impact elasticity? 2.4 Units of Measurement and Functional Form • Consider the following model:where the number of squirrels and trees are in single unitsif trees=2000 then the predicted number of squirrels becomes 1500if there are no trees, there are 500 squirrelshow does this change if squirrels are measured in hundreds (ie: divided by 100)? (ie) 5 . 500 ˆ i i trees rrels i squ + = 2.4 Units of Measurement and Functional FormIf squirrels are measured in hundreds, then zero trees would produce 500 squirrels, so B hat=5 (divided by 100)If there are 2,000 trees, then B 1 hat*2000 must equal 10 (155, or 1,000 squirrels)Therefore B 1 hat=0.005 (divided by 100) (ie) 005 . 5 ˆ i i trees rrels i squ + = 2.4 Acorns are for the squirrels Therefore When the dependent variable is multiplied (divided) by a constant… Multiply (divide) the OLS intercept and slope by the same constant. IE: Change the y – change OLS the same way. 2.4 Units of Measurement and Functional Form • Consider the following model:where the number of treehuggers and trees are in single unitsif trees=800 then the predicted number of treehuggers becomes 900if there are no trees, there are 500 treehuggershow does this change if trees are measured in hundreds (ie: divided by 100)? (ie) 5 . 500 ˆ i i trees ggers u treeh + = 2.4 Units of Measurement and Functional FormIf trees are measured in hundreds, then zero trees would produce 500 treehuggers, so B hat=500 (nothing has changed)If there are 800 trees, then trees=8 and 8(B 1 hat) must equal 400 (900500)Therefore B 1 hat=50 (multiplied by 100) (ie) 50 500 ˆ i i trees rrels i squ + = 2.4 Acorns are for the squirrels Therefore When the independent variable is multiplied (divided) by a constant… Divide (multiply) the OLS slope (not intercept) by the same constant. IE: Change the x – change OLS slope the opposite way. 2.4 Units of Measurement and Functional Form How does R (goodness of fit) change when a 2.4 Functional Form Thus far, we have focused on LINEAR relationshipsLinear relationships don’t capture all of the possible interaction between variablesLinear relationships assume that the first x has the same impact on y as the last xchanging impacts can be captured through the use of NATURAL LOGARITHMS 2.4 LogLin Model2....
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This note was uploaded on 03/14/2009 for the course ECON ECON 399 taught by Professor Priemaza during the Spring '09 term at University of Alberta.
 Spring '09
 Priemaza
 Econometrics

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