Dear All:
I have a dataset that looks at auditor changes and the impact on audit fees. What i need to do is to predict the fees the client would have paid if they did not change auditors and compare this with the actual fees paid to calculate the discount or premium.
To model this came up with the following code.
Companies choose at some point of time which size auditor they want. big or small auditors, either at IPO or some auditor change outside my sample period.
During my sample period companies decide each year whether to change auditors or to stay with their incumbent auditor (big or small auditor).
If companies chose to change they can do one of four things. Change to another auditor of the same size (big to big, or small to small), change to a bigger auditor (small to big) or change to smaller auditor (big to small).
This gives me six choices and so a multinomial logit is in order.
change = 0 if no change, incumbent is big auditor
change = 1 if no change, incumbent is small auditor
change = 2 if change, new auditor is big auditor, incumbent is also big auditor (lateral change)
change = 3 if change, new auditor is small auditor, incumbent is also small auditor (lateral change)
change = 4 if change, new auditor is big auditor, incumbent is small auditor (go up in size)
change = 5 if change, new auditor is small auditor incumbent is big auditor (go down in size)
I am interested in the two lateral changes for calculating the discount of the premium in fees given the change.
So here is what I did.
ran the logistic regression.
mlogit change
ap_reg eu_reg ja_reg yr2-yr10
iicsales age_entry p_cap pf_relcap length scope diff
numfoundries duncert
, basecategory(0) ;
*** Predictions;
predict p0 p1 p2 p3 p4 p5, p;
generate mills_0 = normd(invnorm(p0))/p0;
generate mills_1 = normd(invnorm(p1))/p1;
generate mills_2 = normd(invnorm(p2))/p2;
generate mills_3 = normd(invnorm(p3))/p3;
generate mills_4 = normd(invnorm(p4))/p4;
generate mills_5 = normd(invnorm(p5))/p5;
Calculated the inverse mills ratios Mills_0 to Mils_5
Use the inverse mills ratio in the second stage.
Since I have to find the fees that the change firm would have paid if there was no change I need to look at change = 0 and change = 2 together; and change = 1 and change = 3 together. The way I did this was to first estimate the second stage regression for change = 0 firms and get the coeff estimates.
Use these coeff estimates on the change = 2 firms values of the independent variables and calculate the predicted fees.
Substract the actual fees from the predicted fees and calculate the discount or premium.
The problem is in the estimation and the calculation of predicted fees with regard to the inverse mills ratio.
Here is the second stage regression for change = 0 firms. I use the inverse mills ratio given outcome = 0
Fees = intercept + controls + Mills_0
I get the coeffs on the intercept, controls and Mils_0.
To predict the fees for the change = 2 firms i need to use these coefficients so i do
Pred Fees = Intercept coeff + (Controls * Coeff on controls) + ?
I dont know what to do with the inverse mills ratio. Should I use the coeff on Inv mills ratio Mills_0 or Mills_2 and should I use the coeff on Mills_0 and multiply with the actual Mills_2 to get the predicted fees.
Thanks in advance for your help. Sorry for the long email.
srini
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