What is the sampling distribution of an estimator?

Sampling distributions of estimators. • Since our estimators are statistics (particular functions of random variables), their distribution can be derived from the joint distribution of X1 …Xn. It is called the sampling distribution because it is based on the joint distribution of the random sample.

Is the OLS estimator normally distributed?

OLS Assumption 7: The error term is normally distributed (optional) OLS does not require that the error term follows a normal distribution to produce unbiased estimates with the minimum variance.

What is meant by sampling distribution?

A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.

Why estimators have a sampling distribution?

Question: The reason why estimators have a sampling distribution is that the values of the explanatory variable and the error term differ across samples. in real life you typically get to sample many times. individuals respond differently to incentives. economics is not a precise science.

Why is the OLS estimator normal distribution?

The reason this estimator is normally distributed is that it is a linear function of the underlying error vector (as written in the equation you have shown), which is normally distributed under the model assumptions.

How well the sampling distribution of our OLS estimates approximates the normal distribution will depend on?

How well the sampling distribution of our OLS estimates approximates the normal distribution will depend on: the sample size.

Is OLS estimator a random variable?

Because ^β0 and ^β1 are computed from a sample, the estimators themselves are random variables with a probability distribution — the so-called sampling distribution of the estimators — which describes the values they could take on over different samples.