How unemployment rate is determined?
There are people who are institutionalized, or in mental institutions for example, are they considered when determining this rate?
The way unemployment rate is determined is based on the workforce that are capable of performing a duty or function with no mental illness or physical disability that would make it impossible for these people to work. Having said this, in any country there is a government agency that manages the social welfare including assistance to help people find a job as well as process their unemployment benefits while looking for work. This government agency usually are able to capture the number of people registered as unemployed and that is how unemployment rate is worked out.
Unemployment is difficult for economists to accurately describe, you are right in asking that, because those people you mentioned would not be included in the rate of unemployment. Generally speaking, unemployment is determined only by those that are actively looking for work.
This is tricky simply because there are many other types of people, its not that black and white, for instance, some people work part time or casual and want to work full time but are not considered unemployed. There are many unemployed people who are not looking for work and therefore are not counted either. It is essentially measured by the number of people looking for work divided by the total labour force. This adds difficulty as there are many people in the black market who work but are not considered part of the work force, secondly the ‘grey’ market are volunteers, house workers etc who ‘work’ or contribute to society but are not officially considered employed.