2
$\begingroup$

Suppose I have a variable $y_{i,t}$ which is say a well-being index for individual of type $i$ in month $t$. There are 2 types of individual, $A$,$B$, which are mutually exclusive, and three non-overlapping periods $t1$, $t2$, $t3$, so that the entire sample periods consists of those three periods.

If I want to estimate the mean of $y$ for each type of individual and each period, along with standard errors for the hypothesis that the mean is 0 for that individual type and period, I can either do it normally (selecting the relevant part of the dataset and computing the mean), or I could run a regression:

$y_{it} = \beta_1 D_A D_{t1} + \beta_2 D_A D_{t2} + \beta_3 D_A D_{t3} + \beta_4 D_B D_{t1} + \beta_5 D_B D_{t2} + \beta_6 D_B D_{t4}+\epsilon_{it}$

where $D_A$ equals one if individual is of type $A$ and 0 otherwise, and $D_{t1}$ is 1 if we are in time $t1$ and 0 otherwise. The remaining variables are defined analogously.

My interpretation is that $\beta_1$ is the mean of the dependent variable for individuals of type $A$ in period $1$. Is this the correct interpretation?

Also, is it necessary to adjust the standard errors in any way? Since periods and individual types are mutually exclusive, I assume not.

$\endgroup$
2
$\begingroup$

Your interpretation of $\beta_1$ is correct. It should be pretty easy to verify by comparing the 6 coefficients to the 6 type x period means.

You should cluster the standard errors by individual to reflect that you have repeated observations of the same individuals over time.

$\endgroup$

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.