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From a discussion here, I saw a comment that

Clustered standard errors/variances with clustering at the unit level are equivalent to robust standard errors/variances.

If I am examine at firm level, whether the unit level he mentioned here is "firm"?

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As far as I can see from the discussion there, by unit level they mean the level of the panel variable. What that is depends on your study. It might be firm or individual or country or whatever your panel variable happens to be.

The panel variable is the variable that dictates the spatial dimension of your panel data. E.g if your panel consists of observations on firm level across multiple years, firm is the panel variables. However, if your panel consists of observations on individual employees across different years, then even if you have firm identifier your panel variable would be employee and so on.

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    $\begingroup$ a great explanation, @1muflon1. However, why they use "panel variable" , it is pretty confused, why do not they just use "individual-level" or "spatial level". Because from my point of view "panel data" is a dataset with two dimensions: spatial and time $\endgroup$
    – Phil Nguyen
    Jul 9, 2021 at 22:30
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    $\begingroup$ @BeautifulMindset I am sorry but I don’t know the etymology of this terminology. My best guess is whoever came up with the term did not like Latin? Also be aware that in econometrics and statistics in general for various reasons (like the fact that often empirical techniques develop in parallel to suit each subfields needs) often you will have multiple words describing the same thing. Some authors use dependent and independent variable, some regressand and regressor, some people talk about spatial and temporal dimension some call them cross sectional and time dimension… it’s just best to $\endgroup$
    – 1muflon1 ♦
    Jul 9, 2021 at 22:44
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    $\begingroup$ Get used to all these synonyms $\endgroup$
    – 1muflon1 ♦
    Jul 9, 2021 at 22:44
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    $\begingroup$ a lot of great terminology for me, thanks a heap, 1muflon1 $\endgroup$
    – Phil Nguyen
    Jul 9, 2021 at 22:46
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"Clustered standard errors/variances with clustering at the unit level are equivalent to robust standard errors/variances."

"Unit-level" in this context means "observation-level".

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