How do you know if it's okay for you to make decisions on behalf of your manager in the event of their absence?

It depends whether the situation is daily and ordinary, or if it's a new situation. I personally act on behalf of my manager regularly with his authorization. It's better to have a meeting and ask for your limits of power and authority when he/she is not available. 

Making a decision while Manager is off is good as long as you got a approval or confirmation on behalf of the Manager, one of the reason is you can solved and finished the problem may occur, but when you face a matter that only  your Manager is required, then i suggest to send an email and wait till he reply to avoid blame happen, in addition to this, while sending mail always mentioned on behalf of your Manager so that the the concerns are aware, regards...

Thanks 

Yes it is ok, when 

- Employee authorized

- Situation require someone to make decision

Otherwise it is not ok, since the employee will hold the responsibility of bad or not suitable decision    

The company policies should mention what should be done in case of the manager's absence.

While taking a decision on behalf of your manager or immediate boss, it is essential to keep in mind the policies of the organisation, the situational realities and also put yourself in the shoes of the concerned senior and first analyse what their reaction would be. It is also important to keep in mind the factors that will be affected by the decision. Taking into consideration all the factors and also the policies and the individuals' outlooks, it would be appropriate to take a decision on behalf of the senior manager, in his absence. It is also important that you validate the decision and update your management accordingly. 

This depends on several parameters:

1. The functional organization of the company
2. Of the Rules of Procedure
3. The nature of decisions "repetitive decisions, requiring uncomplicated information or complex information
4. The distribution of decision-making powers
5. Your power, your functions, your responsabilities and your limits
6. your skills
7. Your personality and abilities
8. Your experience
9. Situations, the nature of the problems, the operations
10. Ability to cope with failure
11. cold blood
12. Sense of responsibility
13. Ability to think before deciding
14. Your judgment "critical mind"
15. The relevance of the information collected
16. Your reputation as a connoisseur in the field
17. Your proposal to solve the problem
18. The maturity of the members of the group or other employees
19. Your hierarchical position
20. The quality of the proposed solutions
21. The degree of uncertainty
22. The degree of complexity
23. The degree of indecision
24. Your ability to decipher the situation and detect problems
25. Your intuition
26. state of mind
27. The required level of abilitation
28. delegation
29. Your control of the situation
30. Your problem-solving skills
31. Your mental process
32. Your influence on others
33. Your ability to argue to convince you of the correctness of your decision
34. Your reaction to events, problems
35. The fertility of your brain
36. Your intelligence
37. Your relationship with colleagues

If manager is not available, will try to contact him thru phone, if not available, will do a skip level meet with my managers manager, if still no go, then is the time for some action which will be within the companys policy, keeping integrity in mind, the decision should be on behalf of the progress/profit of the company at the same time should have a happy customer. Need to think what the manager would have done at this point, also need to think about the outcome on this and update the management as available

Decision on behalf of the Director will consider disobeying him unless summits Asked First in this or take authorize him to do so, then evaluating these decisions before consulted by telephone on the Least because he will be seen as a matter of transcendence him or rebellion sooner or later, and if it did not object once it is not that means he will never objected.

If the situation is urgent, the employee shall make a  decision and MUST inform his manager in writing upon his arrival stating the situation

By being very clear on my delegated powers in advance of my managers absence

Dear sir To Be a good and make more improvements in myself & my skill with help of professional expertise. Hence to serve your esteemed Organization with utmost loyalty & sincerity. I am looking forward to strengthen my interpersonal skills and improve my English communication skills, along with building a firm bright career in the. For which I am willing to work full time in a dynamic environment.