Econ1150 - PS4
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Econ1150 - PS4
Due: Wednesday, April 12, 10:30AM
1. According to a particular economist, the production of a certain commodity y only needs two inputs, labor L and capital K. However, the productivity of each factor also depends upon some unobserved random factors (e.g. ”luck” or ”entrepreneurial skill”), so that the economist thinks that the production function can be described by the following equation
yi = Li(a)Ki(8)εi (1)
where α , β > 0, and εi represents the unobserved/random component. The economist draws a sample of n independent and identically distributed observations (Li , Ki , yi ), each one describing inputs and output of the i-th production process. The economist is interested in estimating the parameters α and β assuming that E[log ci | Li , Ki] = 0.1
(a) Equation (1) as it is (that is, without any transformation) cannot be used to estimate the param- eters of interest α and β using OLS. Explain why.
(b) Given all the information you have, can you compute E[ci | Li , Ki]? If yes, compute it, if not, explain why you can’t do it.
(c) Describe how you can transform equation (1) in a useful way to estimate the parameters α and β using OLS.
(d) Once you have transformed equation (1), prove that the OLS linearity assumption holds in your modified model. That is, prove that the expectation of the error in your modified equation, conditional on the regressors, is equal to zero (Hint: this is trivial if you have correctly solved the previous steps. If your solutions involve complicated arguments/calculations, you are surely on the wrong track).
(e) What is the economic interpretation of the estimated parameters α and β ?
(f) According to economic theory, the production function described in (1) exhibits decreasing, con- stant, or increasing returns to scale if α + β is, respectively, < 1, = 1, or > 1. Describe at least two alternative ways to test the null hypothesis that the production function exhibits constant returns to scale.
2. The following data, taken from Forbes Magazine’s 1996 survey of CEO (chief executive officer) com- pensation, contains information on CEO compensation at 770 publicly traded firms. Each firm in the
dataset had only one CEO in 1996. For each of the 770 firms in the dataset, we observe:
Salbon - The CEOs salary plus bonus (in 1000s of dollars)
Logsalbon - The natural log of the CEOs salary plus bonus (in 1000s of dollars)
Logsales - The natural log of the firm’s sales in 1996 (in millions of dollars)
Fiveret - The firm’s five year average total return (in percentage)
Age - The CEOs age in 1996 (in years)
Grad - A dummy variable equal to 1 if the CEO attended a post-graduate program (e.g. MBA), 0 if not
Computer - A dummy variable equal to 1 if the firm is in the computer industry, 0 if not Financial - A dummy variable equal to 1 if the firm is in the financial industry, 0 if not Here are the results of a regression of Logsalbon on the covariates:
LogSalbon = 3.65+ .31 LogSales+ .0016Fiveret+ .014 Age-.037Grad-.0037Computer+ .156 Financial
( .25) ( .019) ( .0012) ( .003) ( .039) ( .064) ( .049)
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R = .32
Here are some tests of a few joint hypotheses:
H0 : β2 = β4 = 0, F-statistic = 1.423
H0 : β2 = β5 = 0, F-statistic = 1.026
H0 : β4 = β5 = 0, F-statistic = 0.473
H0 : β2 = β4 = β5 = 0, F-statistic = 0.959
(a) People frequently complain about the high salaries and bonuses earned by CEOs. Some suggest that their compensation is almost totally disconnected from the performance of their firms. Using the company’s five year return (Fiveret) as a measure of a firm’s performance, do you find evidence that CEO’s are rewarded for good performance? What effect do you find? Justify your answer.
(b) Do CEO’s at larger firms earn higher salaries? If so, how much? Justify your answer using LogSales as your measure of firm size.
(c) Do the data provide any evidence that CEO’s receive a premium (i.e. higher earnings) for having attended a post-graduate program? What effect do you find? Explain.
(d) Suppose I re-run the regression using Salbon instead of LogSalbon as the dependent variable and
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find that R = .34. On the basis of this evidence, should I conclude that it’s better to run this new regression instead of the earlier one? Explain.
2023-05-02