What are some reasons why CEOs make 200-1000x as much as post PhD researchers?

Your question contains several false claims. I will give you benefit of doubt and assume those falsehoods are not intentional and just reflect lack of statistical literacy and misunderstanding/misreading of underlaying materials you link, but since no coherent logical argument can be made arguing from false premises I will first correct those false arguments before answering the question.

Addressing False Claims

1. You state:

Alongside that, the average CEO makes only around 200x that of the average Post PhD researcher.

False. First, these numbers will differ among countries and time, but lets use USA as an example. According to the same website that you use for most current average PhD salary ($50,000) in USA, the most current average CEO salary is $214,000.

Hence on average CEO salary is only about 4x higher than PhD researcher salary.

The way how you arrived 200x figure (which itself is arithmetically wrong as 14mill/50k=280 not 200) makes no sense statistically or even economically. You cannot just compare average PhD compensation across all PhD's with average CEO compensation at the top 350 public firms (the only source that has 14 million average statement is that report which explicitly states this is for top 350 public firms). Anyone could just cherry pick some small group of high income scientist such as only those scientist who won Nobel Prize, whos compensations are high and then compare it to the $200k average for all CEOs and then ask why are PhD's paid more than CEOs. This is simply, from statistical perspective so incorrect on such a basic elementary level that I don't even know what more to say about it. This extremely gross misuse and abuse of statistics. If you want to compare average CEO and PhD pay you have to do it for whole population and not just cherry pick the best paying CEOs from best firms and compare them to all PhDs everywhere.

When it comes to 'max pay' pay for CEO and PhD you are just randomly picking two people that happened to have articles written about them so there is no indication whatsoever those are respective 'max pays' as you put it for those two professions. To determine that you would need some statistics which gives you fuller picture of income distribution in the professions. Hence, nothing in your sources supports the claim that the difference between the highest payed PhD and CEO is 1000x. It might be higher or lower but stating it is 1000x based on the articles makes no sense.

2. You state:

The fact that CEOs have so much money in their own appreciating assets means that market forces drive their incomes up because in order to pay them a competitive salary that would make them want to work there it needs to compete with the appreciation of their stock assets. So their appreciating assets are driving inequality by detaching their pay from the amount and quality of their work. Here's an article on the increase in CEO pay to support my idea here.

No I read the paper very carefully and it does not contain any support for your idea, but reading the paper I think I understand why you might think it does.

The paper claims that large portion of pay inequality stems from stock options and increase in stock prices. But this has nothing to do with your idea - in fact it actively contradicts your idea.

Stock options mean that you are allowed to buy stocks at some predetermined price regardless of what market price of the stock is. For example, a company A could allow executive X to purchase in a current year 1000 units of its stock for $10. Now this option exists irrespective of market value of the stock so if the stock raises in value during the year and it is worth $100, then executive might exercise this option, purchase these stocks for $10 sell it for $100 and get extra income of $90 text{x}1000= 90000$.

Now this is considered to be part of CEO total compensation (i.e. compensation including all benefits), but if anything this stock option lowers the actual monthly salary not increases it. In labor economics it is well established that firms use these sort of benefits (e.g. stock options, company car, company house/apartment etc) because using those benefits allows them to pay less for their employees (see Borjas Labor Economics). For example, consider following situation an employee has two job offers one that offers $10000 per month as a salary, second company offers $9000 as a salary + company car. Now if person values company car at least at $1000 they will pick the later option, and this can be much cheaper for company that has unused extra car. The same way stock options are firms way of how to reduce the actual salary of their executives and they certainly do not drive it up.

Answering Question Why CEO's Earn More on Average

Well this boils down to a question why there are any differentials between different professions. There are several answers to that in economic (see Borjas Labor Economics):

1. Marginal productivity differs between professions: No matter whether you have PhD or you are CEO your pay in the long run will have some relationship with marginal productivity (a competitive firm cannot afford to pay you consistently way more than your marginal product or it would loose money on employing you - that is not viable in long run).

   Now when most people think of productivity they will think of how fast people work, but actually the productivity is the value of output over inputs. Hence person who can make one work of art worth 10 millions in one week is still more productive than person who can make 1 million of paintings that are considered to be worth just $1 each.

   Given that executives job is to direct the resources of whole company their work will have high value since for example, increasing efficiency of production through better managerial practice by $1 per-product can mean millions of dollars of savings if you are producing millions of products. As firm become more larger even very small difference in productivity or effort or talent can lead to very large differences in how much CEO's contribute to company's profit (Gabaix & Landier, 2008).

2. Compensating differentials - compensating differential the additional amount of income that a person must be offered in order to motivate them to accept a given undesirable job, relative to other jobs that worker could perform. For example, garbage workers are often pay way more than other similarly skilled workers which reflects the fact that working as a garbage worker is extremely unpleasant.

   As someone who works in academia I can tell you that working as a researcher is a passion and I would be willing to do this work even for half of my current pay. Working as CEO might be much less pleasant and satisfying. Also, culturally many children are told from young age that being scientist is virtuous (same as firefighter/doctors etc). This is less so when it comes to being an executive which is by many seen as less virtuous profession (how many kids dream of becoming CEO of auditing company?).

3. Institutional issues/Bargianing - Especially in cases where there is less competition in industry, company might earn abnormal profits that then can be considered 'quasi' rents - in such cases the point 1 applies less perfectly, and workers can get paid more than their marginal product depending on their bargaining power. It is possible that CEO's have better bargaining power than other employees or in this context PhD researchers. This depends on exact institutional setting and context (for example unions increase bargaining power of workers).

4. Agency problems: When it comes to executives working for corporations there are several agency issues as they are leaders of a corporation that often they themselves do not own (most CEO's wont own significant portion of a company) and hence they have incentive to try to increase their pay at the expense of the organization (see Bebchuk and Fried 2003).

   To address this issue most corporations will have board of directors that is supposed to 'watch' the CEO, but this is imperfect solution and it is argued that depending on how well the top structure of organization is designed CEO's can still manage to increase their pay above what would be justified otherwise.

There are also bunch of other issues, this question is simply too broad to address every single factor that contributes to difference between CEO pay vs any other profession. For example, some of it is driven by the 'superstar' effect (Elson & Ferrere, 2012). When looking at the total compensation not just salary as the paper you cite the fact that options are nowadays way more valuable due to relatively large increases in stock prices is one factor as well when we talk about total compensation including all benefits rather than just salary itself (but again this has nothing to do pay having to increase to match increase in stock prices - it is because options mean that CEO's can earn extra income by arbitraging stocks and if anything this actually lowers their salary excluding the option).