Benefits available for the Social Security Number vs. the ITIN:
- Child tax credit. You can receive $2000 for your 9-year old daughter instead of $500 (if you qualify otherwise). A dependent with an ITIN cannot receive this benefit.
- Recovery Rebate Credit. This credit is discussed by @NCperson
- Earned Income Credit calculation. Whether or not you receive earned income credit will depend on whether you (and your spouse, if married) also have a Social Security Number, as well as the amount of earned income you claim in 2020.
No additional benefits are available to a dependent with an ITIN as compared to a Social Security Number. But even if there were no other benefits, once an individual receives a Social Security Number, their ITIN is no longer valid. So to claim your daughter as a dependent for any benefit, you must use her Social Security Number, because her ITIN is no longer valid.
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