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We have discussed in class the fact that asymptotic theory enables us to simplify the requirements...

We have discussed in class the fact that asymptotic theory enables us to simplify the requirements for OLS analysis and hypothesis testing.

Your friend is taking econometrics for the first time, and is confused about the difference between asymptotic normality and asymptotic efficiency. Explain to him what each of those phrases mean.

Math   Statistics-And-Probability   
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Answer #1

Here we have to discuss two concepts such as asymptotic normality and asymptotic efficiency. The condition of normality is not proved always and that’s why we need to use the concept of asymptotic normality. We know that an asymptotic distribution is a probability distribution from a sequence of distributions. If the distributions under study do not follow exact normal or approximately normal distribution, then we consider the sequence of these distributions which follows or converges to the approximate normal distribution. The week normality from a sequence of distributions is called as asymptotic normality.

If we found that the sequence of distributions has asymptotic normality then we can calculate the efficiency of the different parameters by assuming the asymptotic normality. This type of efficiency estimated from asymptotic normality is called an asymptotic efficiency.

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