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# st: Defining a New Function. Maximum Likelihood Modelling in STATA

 From XandeR XandeR To statalist@hsphsun2.harvard.edu Subject st: Defining a New Function. Maximum Likelihood Modelling in STATA Date Fri, 22 Aug 2008 19:10:16 +0400

```Hello.

I am currently writing an MSc dissertation which is aimed to derive a value function of money. This involves analysis of the data from TV show "Deal or no Deal". The model I am currently trying to adopt is based on the paper by Post et al "Deal or No Deal? Decision Making under Risk in a Large Pay-off Game Show".

I am new to the STATA programming (first started two weeks ago). So far I am successfully completed generating all required variables for the model. However I feel that I will be unable to learn how to make the model myself in time (the deadline for submitting dissertation is 15th September). I would greatly appreciate any help you can give me on this matter; particularly I am stuck with defining value function mentioned below. If you are interested to help me please do not hesitate to contact me if you require any further explanation or have any questions. This is my project I have done in the past for another module where the model is explained in details:

https://files.warwick.ac.uk/oshevchenko/files/!Behavioral Project.pdf

If you cannot or don't want to download the file here is this model is briefly introduced (to the best of .txt format)

The model adopts Kahneman and Tversky's Prospect Theory Utility function, which is:

V(X|RP)=-lambda*(RP-X)^alpha if X<=RP
V(X|RP)=(RP-X)^alpha if X>RP

Where lambda, RP and alpha are parameters to estimate and X is amount of money. In case you are not familiar with the concept, value function calculates value a person attaches to amount of X, given a reference point (RP).

The model is panel-data probit with likelihood function:

L(X_ir)=normprob((cv(X_ir)-sv(X_ir))/(delta(X_ir)-sigma)) if "No Deal" (variable deal=0)
L(X_ir)=normprob((sv(X_ir)-cv(X_ir))/(delta(X_ir)-sigma)) if "Deal" (variable deal=1)

Where X_ir - is an observation of contestant "i" at round "r",

sv(.)=V(.|RP) is called stop value, which is value of bankers offer (named "offer" in my dataset)

cv(.)=pr*sum[V(.|RP)] - an average of values of all possible banker's offers in the next round. "pr" is probability to have each offer in the next round. For example at round 1 there are 17 boxes in the game, while moving into round 2, contestant opens 3 more boxes and ends up with 14 boxes in round 2. Therefore in round 1 there are 17!/(14!*3!)=680 possible offers in the next round. So pr here will be 1/680. I have already generated all the predictions needed. There are 680 variables called offer_hat`i' in my dataset now.

delta(.) is called difficulty of decision parameter, which is argued to influence error of the decision and therefore is used to weight observations.
delta(.)=sqrt(pr*sum(V(.|RP)-cv(.))^2)

sigma is a white noise parameter.

Thank you very much indeed.

Regards

Alex

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