It was all by accident I realized that how important random numbers are in understanding Statistics and Econometrics. The random number which is embedded with the sense of Probability acts as a fundamental understanding of Econometrics.
First let us refresh our understanding of Probability. What is Probability? It's an answer that mathematicians have been suffering for ages until Kolmogorov introduced the concept of Probability Space in the 1930s. It is like an architect of all discussions related to Probability. (omega,sigma-field,Pr) sigma-field is many times deemed as events which are combinations of components in omega (the so called sample space) and Pr is a function that mapping the sigma-field to a real line between [0,1] given the fact that sigma-field is Borel-measurable. In words, Pr measures how likely sigma-field is going to happen under omega.
It looks mathematically intimidating while the fundamental idea is rather straightforward (but somehow it took me a year to understand). Just as you have to figure out a 2-dimensional graph on a paper, you would need to apply means such as (X axis and Y axis or polar axis). If you want to figure out something in terms of probability you need coordinators as well. There comes the definition of Probability Space.
Now coming back to our main idea about Random Numbers.
We are not going to discuss about the generation of RN which is quite an important field in Math. But we are going to share some lights that I have on RN.
RN is act as an important input of Statistical or Econometric experiments since it is perceived as a random draw From the assumed distribution. In other words by drawing RNs you are able to form a sample From the population. And given the fact that RNs should be attached with probability (otherwise why should we call them "Random") all your experimental outcomes which are your estimators should be attached with probability. And that is the mathematical reason of central limit theorem.
In Econometrics, if you perceive the Economy as a fundamental system with certain "Random" shocks, you are actually borrowing the idea of "RN". And by this assumption you are doing all those fancy Econometric Estimation or Statistical Estimation. So Keep in Mind: what you are estimating is nothing but a RN with certain distribution. You don't know what is the truth, you can only conjecture the truth. Saying b is significantly different From 0 under 95% confidence intervals is not equal to that the real b isn't 0.
The idea of the usage of RN lies in line with those Scientific Experiments in laboratory. Statisticians also want to do experiments but instead of physically but logically.
The RN again shed lights on the understanding of Probability which in my opinion is of most importance in academic researches related to Econometrics and Statistics. Besides it is also a philosophy of understanding the world since collateral ideas could also be found in religious or philosophies. An example would be “听天由命” 