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From |
"Alexis Belianin" <albelix@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: ml probit with nonlinear argument(s) |

Date |
Mon, 29 Sep 2008 14:19:28 +0400 |

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 albelix@gmail.com * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: ml probit with nonlinear argument(s)***From:*"Eva Poen" <eva.poen@gmail.com>

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