HW2a(1) - Econ 4010 Introduction to Econometrics(Spring...

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Econ 4010: Introduction to Econometrics (Spring 2016) Homework 2 Answers Olivier Parent ( [email protected] ) Assignment 1. A standard ’money demand’ function used by macroeconomists has the form ln( m ) = β 0 + β 1 ln( GDP )+ β 2 R , where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of the nominal interest rate measured in percent year. Suppose β 1 = 1 . 5 β 2 = - 0 . 04. What will happen to m if GDP increases by 1% ( R is held constant)? What will happen to m if the interest rate increases from 3% to 4% ( GDP is held constant)? A 1% increase in GDP means that ln( GDP ) increases by 0.015. The implied change in ln( m ) is 1 . 0 × 0 . 015 = 0 . 015,which corresponds to a 1 . 5% increase in m . With R measured in percentage points, the increase in R is from 3.0 to 4.0 or 1.0 percentage point. This leads to a change of ln( m ) of - 0 . 04 × 1 . 0 = - 0 . 04, which corresponds to a 4% fall in m . 2. Sales in a company are $201 million in 2004 and increase to $205 million in 2006 (a) Compute the percentage increase in sales. Compare this value to the logarithm approximation. The percentage increase in sales corresponds to: (205 - 201) / 201 = 0 . 0199 or 1 . 99%. The logarithm approximation is equal to: ln(205) - ln(201) = 0 . 0197 or 1 . 97%. These two results are identical.
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(b) Repeat twice the previous question assuming Sales 2006 = 210 and Sales 2006 = 500.
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