7. A researcher models the relationship between the expenditure of a company, S, in period t...
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7. A researcher models the relationship between the expenditure of a company, S, in period t and the expected profit, +1, in period t +1 as follows: St= Bo + B₁+1+B₂re + U₁ (7.1) where r, is the borrowing interest rate set by the central bank (measured in percentage) and is an i.i.d. error term with E(ut St-1, St-2, Rt, t-1,..., Tt, Tt-1,...) = 0. The expected profit is determined by the following adaptive expectation process: ni+1-ni =0(-i). where πt is the actual profit realised at time t. Using quarterly data from a US company, the researcher obtains the following estimates from using OLS: S = 0.36 +0.94 -34.65r+ 0.65 S-1, (0.142) (0.54) (0.85) (2.85) n = 240, R² = 0.56. Hint: Use (7.1) and (7.2) to express S, as follows: (7.2) (a) (6 marks) What is the interpretation of in (7.2)?. Using the regression results in (7.3) obtain an estimate for 0. St=a0+ a1 + a2 + a3S-1 +₂₁ (7.3) (7.4) where = -(1-0)-1- (b) (5 marks) You are concerned that the estimate for obtained in (a) is not suitable. Demonstrate formally that the OLS estimator of (7.4) will be inconsistent. Hints: You are not expected to look at the consistency proof for the a parameters explicitly. (c) (4 marks) Discuss how you can use an IV estimator to obtain a consistent estimator for the a parameters and hence obtain a consistent estimator for 9. 7. A researcher models the relationship between the expenditure of a company, S, in period t and the expected profit, +1, in period t +1 as follows: St= Bo + B₁+1+B₂re + U₁ (7.1) where r, is the borrowing interest rate set by the central bank (measured in percentage) and is an i.i.d. error term with E(ut St-1, St-2, Rt, t-1,..., Tt, Tt-1,...) = 0. The expected profit is determined by the following adaptive expectation process: ni+1-ni =0(-i). where πt is the actual profit realised at time t. Using quarterly data from a US company, the researcher obtains the following estimates from using OLS: S = 0.36 +0.94 -34.65r+ 0.65 S-1, (0.142) (0.54) (0.85) (2.85) n = 240, R² = 0.56. Hint: Use (7.1) and (7.2) to express S, as follows: (7.2) (a) (6 marks) What is the interpretation of in (7.2)?. Using the regression results in (7.3) obtain an estimate for 0. St=a0+ a1 + a2 + a3S-1 +₂₁ (7.3) (7.4) where = -(1-0)-1- (b) (5 marks) You are concerned that the estimate for obtained in (a) is not suitable. Demonstrate formally that the OLS estimator of (7.4) will be inconsistent. Hints: You are not expected to look at the consistency proof for the a parameters explicitly. (c) (4 marks) Discuss how you can use an IV estimator to obtain a consistent estimator for the a parameters and hence obtain a consistent estimator for 9.
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Related Book For
An Introduction to Management Science Quantitative Approaches to Decision Making
ISBN: 978-1111823610
14th edition
Authors: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
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