Does the investment component of GDP (demand side) identity include expenditures by the government and households?
“I” would be called private domestic investment. (https://apps.bea.gov/iTable/iTable.cfm?reqid=19&amp;step=2#reqid=19&amp;step=2&amp;isuri=1&amp;1921=survey)   

Firm and household expenditures for investment both count as private investment. 

(https://courses.lumenlearning.com/boundless-economics/chapter/measuring-output-using-gdp/)

Any investment expenditure by a government would be categorized under government spending. 

If a government builds a school or bridge it would go under government spending “G”. (https://courses.lumenlearning.com/wm-macroeconomics/chapter/calculating-gdp/)