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From |
efeijen@worldbank.org |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: User-defined MLE problem: How would you solve this? |

Date |
Wed, 18 Jun 2008 12:32:44 -0400 |

Hi: I would appreciate your help on the following MLE problem (it is the transaction cost model for financial markets as initially used in Lesmond (1995)). Please see the problem description below. Many thanks for your help! Erik This is the log likelihood function: LNF= SUM(if y_j<0) [ln(1/(2*pi*(sigma_j^2)))-(1 /(2*(sigma_j^2))*(y_j+c1_j-b_j*x))^2] + SUM(if y_j>0) [ln(1/(2*pi*(sigma_j^2)))-(1 /(2*(sigma_j^2))*(y_j+c2_j-b_j*x))^2] + SUM(if y_j=0) [Ln(NCDF((-c2_j-b_j*x)/sigma_j)- NCDF((-c1_j-b_j*x)/sigma_j)]. Where the y_j's and x vectors represents the dependent and independent variables, respectively. NCDF stands for normal cumulative density function. The parameters c1_j, c2_j (constants), b_j (x-coefficient), and sigma_j need to be estimated for each dependent variable j. Below you find the .ado file and the command I used for this problem. However I know they are not correct, since my setup estimates 2 x-coefficients defined by the mu1 and mu2 equations, but I only want to estimate one for the dependent variable j: b_j. What to do such that the intercepts in mu1 and mu2 are different, but b_j are identical? program LDV version 9.2 args lnf mu1 mu2 sigma quietly replace `lnf'=ln(1/(2*_pi*(`sigma'^2)))-(1 /(2*(`sigma'^2))*($ML_y1-`mu1'))^2 if $ML_y1<0 quietly replace `lnf'=ln(1/(2*_pi*(`sigma'^2)))-(1 /(2*(`sigma'^2))*($ML_y1-`mu2'))^2 if $ML_y1>0 quietly replace `lnf'=ln(normalden(-`mu2',0,`sigma')-normalden(-`mu1',0,`sigma')) if $ML_y1==0 end Stata command: ml model lf LDV (mu1: y=x) (mu2: y=x) (sigma:) * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: User-defined MLE problem: How would you solve this?***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

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