0
$\begingroup$

I have a question that contains a list of parameter estimates and their related standard errors. It then goes on to ask that I explain how I know all parameter estimates are statistically significant at a 5% significance level, but without performing any 'sophisticated calculations'. Does this mean I have to compare the standard errors to the estimators or do I find their t-values?

$\endgroup$
3
$\begingroup$

Normally an exam question like that can be solved by simply calculating the $t$-statistics which can be simply done as:

$$t_{\hat{\beta}} = \frac{\hat{\beta}-\beta_0}{se(\hat{\beta})}$$

where $\hat{\beta}$ is the estimate, $\beta_0$ is the assumed value of beta under null (usually 0) and $se(\hat{\beta})$ standard error of the coefficient and then compare it to $5\%$ critical value (for large $n$ and two sided hypothesis approximately $1.96$).

However, you should ask your teacher/supervisor to clarify what is considered 'sophisticated calculation' - some might consider even subtraction and division sophisticated. An approximate rule of thumb that requires even less calculation is to see if the coefficient $\hat{\beta}$ (and assuming null hypothesis assumes $\beta_0=0$) is twice as large as the standard error.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.