If there was not enough collected at closing can we do an analysis right after closing so that it will not cause a deficiency at the first disbursement?

Review 3500.17 (i.e. (i)(4)). This discusses when a short year analysis can be performed.

does it matter that no payment has been made yet also it does not say whether a short year statement can be used to correct an error do you believe this can be done?

IMO the short year statement cannot be used to correct your error. However, that doesn't prevent you from admitting your error and giving the borrower the option to voluntarily make up the difference now either in a lump sum or increased monthly payments or wait until the annual analysis and make it up then.

should we do one when a deficiency occurs even though it is not at the end of the computation year?

No.

thanks

When a loan balance is reduced to 80% of the original value and the borrower requests that MI be dropped, can a lender run a new escrow analysis and apply MI funds to other escrow buckets (tax or hazard insurance) or must the amount held in the MI escrow bucket, plus any refund from the MI company, be reimbursed to the borrower?

Interesting question. I really don't have an answer. The general rule is you can never apply escrow funds to anything. It's not your money. But it makes sense to apply escrow balances to other escrow items.

I would should analyze the account and issue a short year statement - in affect, applying excess MI amounts to the other escrow items.

See the Homeowners Protection Act Section 4902(f). You must return the premiums to the borrower within 45 days.