Dear Statalisters,
I am trying to estimate the parameters of individual utility function
under risk using -ml- command in Stata 9.2 (updated). The model is
probit: the lhs codes individual preferences in a sequence of pairwise
choices from the set of lotteries of a form [p_1,x_1; p_2,x_2;
p_3,x_3] vs [q_1,x_1; q_2,x_2; q_3,x_3], where p's and q's are
probabilities, and x's are outcomes.
The EU theory says that choice depends on whether p_1*u(x_1) +
p_2*u(x_2) + p_3*u(x_3) is greater or less than q_1*u(x_1) +
q_2*u(x_2) + q_3*u(x_3). I estimate the parameter(s) of the u function
of a specified form – say, a power CRRA function u(x_i)=(x_i)^\alpha.
Normalizing utilities and defining d_2=p_2 – q_2, d_3=p_3 - q_3, the
probit specification is Prob(y=1|\alpha) = \Phi( d_2 +
d_3*(x_3)^\alpha ), where \Phi is standard normal cdf, whose value
depends on known d_2, d_3 and x_3, and the parameter \alpha to be
estimated.
How should I fit this model in Stata? Statalist and guides, including
Gould e.a. book on -ml- do not seem to contain straightforward hints.
My guess is something like
program define pcrra
version 9.2
args lnf alpha
tempvar xb
gen double `xb' = d3*x3^`alpha'+d2
quietly replace `lnf'=ln(normal(`xb')) if $ML_y1 == 1
quietly replace `lnf'=ln(normal(-`xb')) if $ML_y1 == 0
end
. ml model lf pcrra (alpha: y= )
. ml check
. ml maximize
This is what I got:
initial: log likelihood = -35.802634
rescale: log likelihood = -34.554852
Iteration 0: log likelihood = -34.554852
Iteration 1: log likelihood = -34.551539
Iteration 2: log likelihood = -34.551469
Iteration 3: log likelihood = -34.551469
Number of obs = 50
Wald chi2(0) = .
Log likelihood = -34.551469 Prob > chi2 = .
----------------------------------------------------------------------------
y | Coef. Std.Err. z P>|z| [95% Conf. interval]
--------+----------------------------------------------------------
_cons |-.37933 1.4415 -0.26 0.792 -3.2046 .4459
-------------------------------------------------------------------------
I suspect this is wrong, not least because of no values of Wald
statistics; but the outcome is qualitatively the same on different
(e.g. larger) datasets. Any suggestion on how to proceed with this
estimation?
Thanks in advance,
Alexis Belianin
[email protected]
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