Exceeded or exceeding

Question

This is a sentence extracted from a book named “Into thin air”:

I’d written more than sixty pieces for Outside over the previous fifteen tears, and seldom had the travel budget for any of these assignments exceeded two or three thousand dollars.

I don’t know why it is exceeded but not exceeding. According to Oxford dictionary exceed something means to be greater than a particular number or amount and this is the example offered:

The price will not exceed £100

Therefore, in the sentence above, I would expect it is:

[...] seldom had the travel budget for any of these assignments which exceeded two or three thousand dollars.

When a reduced relative clause is used, it should be

[...] assignments exceeding two or three thousand dollars.

I wonder whether that is the causative form “have something done” in the origin sentence but I still can’t make out why they use it.

Answer 1

This is not a relative clause, it's just a normal phrase in the past perfect tense. It's just the word order that's confusing; a more simple ordering would be:

The budget for these assignments had seldom exceeded two or three thousand dollars.

Answer 2

It isn't "exceeding" because this whole line is in the past-perfect tense (sometimes called the "pluperfect"). The word order is a bit confusing, but we could untangle it and remove some unnecessary clauses to come up with

Over the previous fifteen years, the travel budget had seldom exceeded two or three thousand dollars.

The author sets a reference time by saying "over the previous 15 years" -- we read that as having a reference time at the end of the period -- and then the travel budgets for each of those works took place during that 15 year period, prior to the reference time, or in the past from a reference point in the past, so the past-perfect is required.

In the past-perfect tense, you use 'had' plus the past-tense verb.

The only way you could use a present-tense verb in that phrase is if it related to some action happening at that before-the-past point: "I had seen the criminal running away from the house."

In that case, we have the past-perfect in "had seen", and then actions happening concurrently to that act of seeing become present-tense.