There is a dependent variable which is measured in £ and can take the form of £0-£100,000. It is effectively the value of the payment made. If it takes the form of £0 it means a payment was not made (because it wasn't authorised). If it takes the form of any number between £0.01 and £100,000 it means the payment was authorised for that amount.
We are interested in looking at how the value of the payment varies according to other information we hold (independent variables).
One of the proposals being put forward is to use a Tobit model with a lower limit of 0. I haven't worked explicitly with a Tobit model before but I can't see why it is appropriate. Payments cannot be negative. There is no censoring at 0 - those points at 0 are simply those where payments haven't been made.
My intuition is to remove all of the observations where the payment made is £0 and simply to run OLS on the observations where the dependent variable is £0.01 - £100,000.
Is the Tobit approach justifiable? Is it as simple as running OLS on a truncated data set?
Edit - To clarify - my concern on whether the Tobit model is appropriate rests on my confusion as to whether the £0 responses are 'corner solutions.' I appreciate, as an unrelated example, that someone can decide to provide no donation (£0) or a donation (>£0). This is a decision made with respect to their preferences/views. However, a £0 in my scenario is simply an entry to represent the fact that a payment has not been made.
Edit2 - To clarify further:
There are a lot of requests for payments which come to us. These all take the form of £0.01 - £100,000. To be paid out, they have to be authorised. Only a subset of the requests are authorised. Those we do not authorise have a payment made of £0.
So we have 2 fields:
- Payment requested - these will also take the form of £0.01 - £100,000. Noone will ever request a payment of £0 as it would be illogical
- Payment made - these will take the form of £0.01 - £100,000 for those payments we did authorise and the form of £0 for those payments we did not authorise. This variable is the focus of our analysis as we want to understand how the value of the payment made varies according to information we hold about the request (i.e. who requested it, what department are they in, what was the request for).
Payments are requested but not authorised because they do not meet eligibility criteria we have in the business. To give a somewhat-related example: someone can make a request for payment of £50 to reimburse an expense they incurred. However, this would fall outside our eligibility criteria and therefore we would not authorise the payment and the payment made would be £0.
This suggests to me the following:
£0 entries in the payment made field are due to our eligibility criteria as a business. £0.01 - £100,000 entries in the payment made field are due to information we hold about the payment itself.
The typical example I see for 'corner solutions' is charitable giving by an individual. Here, the decision to give £0 or >£0 are both decisions made with respect to the characteristics of the individual.
I am curious thus if the 'corner solution' approach still applies to my scenario. The characteristics which determine the size of the payment made and the characteristics which determine whether we authorise payments are not necessarily the same characteristics.