一个小习题，希望通过讨论加深对固定效应以及随即效应模型的理解

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• Suppose you are acompensation consultant who is analyzing CEO compensation in public companiesover the last two decades. Each observation is indexed by firm i, CEO j, andyear t:

  Compensationi,j,t = β1FirmChari,t + β2FirmChari + β3CEOCharj,t + β4CEOCharj +αi +αj +αt +"ijt,

  where “Char” stands forcharacteristics. Potentially you can use any information disclosed in a firm’sForm 10-K and annual proxy statement (if you have never read or even heardabout such forms, it is time to do self-learning), but it is important to keepthe regression reasonably parsimonious. Your goal is to understand thedeterminants of CEO compensation, and then to assess whether the pay system reflects,on average, meritocracy and market e￠ciency.

  1.         Please specify thevariables from each of the groups (FirmChari,t, FirmChari, etc.)that you would like to include in the regression.

  2.         Please state your prioron whether each coe￠cient should be positive or negative, and explain why.

  3.         Suppose αi and αj are both potentially correlated withunobserved firm/CEO character- istics that might also a§ect CEO compensation.The annual CEO turnover rate is about

  4

  12%. A person mayassume the CEO role in multiple companies sequentially, however, such cases arenot common. Please articulate the regression model that you are going to useand then discuss which coe￠cients you can identify and which you cannot?

  4.         Suppose you learn thata lot of the boards use previous year’s pay as a “base” when deciding the levelfor current year. How does this information a§ect your choice of regressionspecification? If you are now choosing a model that is di§erent from youranswer to previous questions, please discuss.

  5.         You are unsatisfiedwith the fact that it is di￠cult to capture a CEO’s raw intelligencewhich you think should a§ect compensation but cannot be properly captured byany of the existing variables. The best proxy used in the literature, it seems,is the SAT

  score. Suppose youmanage to get individual CEO’s SAT scores, what do you expect the coe￠cient tobe like? Suppose all you can get is the average SAT of the college that a CEOattended during the years s/he attended. How does your answer di§er? Supposeyou includebothSATscoresinthesameregression. Howwouldyouinterpreteachcoe￠cient?

  对于最后两个问题，如何理解
  

                                
                        
               
                                
                        
               

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关键词：固定效应 Compensation Intelligence parsimonious Determinants 模型

Suppose you are a compensation consultant who is analyzing CEO compensation in public companies over the last two decades. Each observation is indexed by firm i, CEO j, and year t:
Compensationi,j,t = β1FirmChari,t + β2FirmChari + β3CEOCharj,t + β4CEOCharj +αi +αj +αt +"ijt,
where “Char” stands for characteristics. Potentially you can use any information disclosed in a firm’s Form 10-K and annual proxy statement (if you have never read or even heard about such forms, it is time to do self-learning), but it is important to keep the regression reasonably parsimonious. Your goal is to understand the determinants of CEO compensation, and then to assess whether the pay system reflects, on average, meritocracy and market e￠ciency.
1.        Please specify the variables from each of the groups (FirmChari,t, FirmChari, etc.) that you would like to include in the regression.
2.        Please state your prior on whether each coe￠cient should be positive or negative, and explain why.
3.        Suppose αi and αj are both potentially correlated with unobserved firm/CEO character- istics that might also a§ect CEO compensation. The annual CEO turnover rate is about
4
12%. A person may assume the CEO role in multiple companies sequentially, however, such cases are not common. Please articulate the regression model that you are going to use and then discuss which coe￠cients you can identify and which you cannot?
4.        Suppose you learn that a lot of the boards use previous year’s pay as a “base” when deciding the level for current year. How does this information a§ect your choice of regression specification? If you are now choosing a model that is di§erent from your answer to previous questions, please discuss.
5.        You are unsatisfied with the fact that it is di￠cult to capture a CEO’s raw intelligence which you think should a§ect compensation but cannot be properly captured by any of the existing variables. The best proxy used in the literature, it seems, is the SAT
score. Suppose you manage to get individual CEO’s SAT scores, what do you expect the coe￠cient to be like? Suppose all you can get is the average SAT of the college that a CEO attended during the years s/he attended. How does your answer di§er? Suppose you includebothSATscoresinthesameregression. Howwouldyouinterpreteachcoe￠cient?

不好意思，直接贴过来，有些乱

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