hw5

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Economics

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Apr 27, 2024

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Introduction to Econometrics - Prof. Brendan Kline - UT Austin Homework #5 Problems 1. Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity ( roe , in percentage form), and return on the firm’s stock ( ros , in percentage form): log( salary ) = β 0 + β 1 log( sales ) + β 2 roe + β 3 ros + u (i) In terms of the model parameters, state the null hypothesis that, after controlling for sales and roe , ros has no effect on CEO salary. Also, state the alternative that ros does affect a CEO’s salary. (ii) Using the data in CEOSAL1.DTA, the following equation was obtained by OLS: \ log( salary ) = 4 . 32 + . 280 log( sales ) + . 0174 roe + . 00024 ros ( . 32) ( . 035) ( . 0041) ( . 00054) n = 209 , R 2 = . 283 By what percentage is salary predicted to increase if ros increases by 50? Does ros have a practically large effect on salary? (iii) Test the null hypothesis that ros has no effect on salary against the alter- native that ros does have an effect. Carry out the test at the 10% significance level. (iv) Would you include ros in a final model explaining CEO compensation in terms of firm performance? Explain. (v) Compute a 95% confidence interval for the coefficient on roe . (vi) Compute a 95% confidence interval for the coefficient on ros . Hint: as discussed for example in example 4.1 in the book, the numbers in parentheses underneath the “estimated equation” in part (ii) are the associated standard errors. This is true basically everywhere in the book. (This question is based on Wooldridge Chapter 4, Problem 2.) 2. The variable rdintens is expenditures on research and development (R&D) as a percentage of sales. Sales are measured in millions of dollars. The variable
Introduction to Econometrics - Prof. Brendan Kline - UT Austin profmarg is profits as a percentage of sales. Using the data in RDCHEM.DTA for 32 firms in the chemical industry, the following equation is estimated: \ rdintens = . 472 + . 321 log( sales ) + . 050 profmarg (1 . 369) ( . 216) ( . 046) n = 32 , R 2 = . 099 (i) Interpret the coefficient on log( sales ). In particular, if sales increases by 10%, what is the estimated percentage point change in rdintens ? Is this an economically large effect? (Remember that rdintens is already measured in per- centage points, so the “units” of the y variable are already percentage points.) (ii) Test the hypothesis that R&D intensity does not change with sales against the alternative that it does change with sales. Do the test at the 10% and the 20% levels. (iii) Interpret the coefficient on profmarg . Is it economically large? (iv) Does profmarg have a statistically significant effect on rdintens ? (Since this question does not directly specify a significance level, think about both α = 0 . 05 and α = 0 . 10.) (v) Compute a 95% confidence interval for the coefficient on log ( sales ). (vi) Compute a 95% confidence interval for the coefficient on profmarg . (This question is based on Wooldridge Chapter 4, Problem 3.) Computer exercises ( Important note: submit your written answers, and also in di cate in your an swer the Stata com mand(s) you used.) 3. The following model can be used to study whether campaign expenditures affect election outcomes: voteA = β 0 + β 1 log( expendA ) + β 2 log( expendB ) + β 3 prtystrA + u, where voteA is the percentage of the vote received by candidate A, expendA and expendB are campaign expenditures by Candidates A and B, and prtystrA is a measure of party strength for Candidate A (the percentage of the most recent presidential vote that went to A’s party). (i) What is the interpretation of β 1 ? (Note that voteA is already measured in percentage points, so this is a level-log model where the units of measurement of y are percentage points.)
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