A manual for writers of research papers, theses, and dissertations, 7th edition - Kate L. Turabian 2007

Use first person pronouns appropriately
Revising sentences
Part I. Research and writing: from planning to production

Almost everyone has heard the advice to avoid using I or we in academic writing. In fact, opinions differ on this. Some teachers tell students never to use I, because it makes their writing “subjective.” Others encourage using I as a way to make writing more lively and personal.

Most instructors and editors do agree that two uses of I should be avoided:

Insecure writers begin too many sentences with I think or I believe (or their equivalent, In my opinion). Readers assume that you think and believe what you write, so you don't have to say you do.

Inexperienced writers too often narrate their research: First, I consulted . . ., then I examined . . ., and so on. Readers care less about the story of your research than about its results.

But we believe, and most scholarly journals agree, that the first person is appropriate on two occasions. That last sentence illustrates one of them: we . . . believe that the first person . ..

An occasional introductory I ( or we) believe can soften the dogmatic edge of a statement. Compare this blunter, less qualified version:

13. But we believe, and most scholarly journals agree, that the first person is appropriate on two occasions.

The trick is not to hedge so often that you sound uncertain or so rarely that you sound smug.

A first person I or we is also appropriate when it's the subject of a verb naming an action unique to you as the writer of your argument: Verbs referring to such actions typically appear in introductions: I will show/argue/prove/claim that X, and in conclusions: I have demonstrated/concluded that Y. Since only you can show, prove, or claim what's in your argument, only you can say so with I:

14. In this report, I will show that social distinctions at this university are . . .

On the other hand, researchers rarely use the first person for an action that others must repeat to replicate the reported research. Those words include divide, measure, weigh, examine, and so on. Researchers rarely write sentences with active verbs like this:

15a. I calculated the coefficient of X.

Instead, they're likely to write in the passive, because anyone can do that:

15b. The coefficient of X was calculated.

Those same principles apply to we, if you're one of two or more authors. But many instructors and editors object to two other uses of we:

the royal we used to refer reflexively to the writer

the all-purpose we that refers to people in general

Not this:

16. We must be careful to cite sources when we use data from them. When we read writers who fail to do that, we tend to distrust them.

Finally, though, your instructor decides. If he flatly forbids I or we, then so be it.