Estimate Fixed-effects model with thousands of groups

Hi all,

I am trying to estimate a simple fixed-effects model that contains a high number of groups. To clarify, the regression I would like to perform should look something like this

In my case I have about 10,000 groups, i.e. i runs from 1 to 10,000; and I have around 4,000 observations for each individual; i.e. t runs from 1 to ~4,000. Within the predictors x I am using roughly 10 variables. Now, I have tried to estimate this regression setup in STATA which works fine using the xtreg function with specifier "fe" for fixed effects. However, I have yet failed to estimate this regression in MATLAB using fixed effects. Estimating it with random effects via "fitlme" and a grouping variable a la (1|GroupingVariable) works fine.

How would I implement this correctly for a fixed effect? Usually, using the categorical function on my grouping variable in this setup will give me an out-of-memory error.

Many Thanks!