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From |
"David Roodman (DRoodman@cgdev.org)" <DRoodman@CGDEV.ORG> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: -cmp- adds multinomial probit |

Date |
Mon, 7 Jul 2008 09:09:37 -0400 |

I have made some significant changes to -cmp-. A short-hand way of describing its current status is to list the commands it can emulate to various degrees: probit, ivprobit, biprobit, oprobit, mprobit, asmprobit, tobit, ivtobit, cnreg, heckman, heckprob, sureg, triprobit, mvprobit, bitobit, mvtobit, bioprobit. ...though its purpose is not to emulate but to allow estimation of a broader variety of models For those unfamiliar with -cmp-: At its core, it is a flexible SUR maximum-likelihood-based estimator that offers a range of models based on the normal distribution, which can be mixed and matched (continuous (OLS-like), probit, tobit, ordered probit, multinomial probit). But it is also consistent for non-SUR models with recursive sets of equations, i.e., ones in which some LHS variables belong in other LHS variables' equations, provided that the equations can be arranged so that the matrix of the LHS variables' coefficients in each others' equations is triangular. As David Drukker helped me appreciate, and as the help file now explains, this estimation framework applies to two broad cases: 1) the true data-generating process is recursive, in which case -cmp- is a FIML estimator; 2) the DGP is not recursive, but instruments make it possible to construct a recursive system, just as in 2SLS, that allows estimation of the structural parameters in the final stage--making -cmp- a LIML estimator. (The last stage may contain more than one equation). The recent changes are: 1) Addition of an (alternative-specific) multinomial probit equation type. This can be used with two different syntaxes: one analogous to -mprobit-; one more like -asmprobit-, in which the user lists a separate equation for each outcome. The help file explains more and includes examples. I am not yet satisfied with the reliability of convergence for the multinomial probit equations models with no restrictions on the covariance matrix. I may need to parameterize this matrix with the Cholesky decomposition instead of or in addition to the lnsig/atanhrho parameterization. 2) Addition of an "lf" mode. -ml-, on which -cmp- is based, accommodates four types of likelihood calculation routine. Till now, -cmp- has been purely a "d1" routine, which calculates likelihood gradients (scores) at each iteration analytically. But "lf" is *sometimes* faster, more precise, or more reliably convergent, as the help file discusses. Most of my -cmp- command lines included either "lf" or "tech(dfp)" (the latter defaulting to d1), but not both. (For problems requiring the GHK algorithm, d1 is almost always better.) 3) Switching to use of ghk2() a new Mata implementation of the GHK algorithm for simulating higher-dimensional cumulative normal probabilities. See http://www.stata.com/statalist/archive/2008-06/msg00323.html. I found this was necessary for -cmp- to work well on multi-equation probit models with many observations and few draws. (Cappellari and Jenkins, Stata Journal 3(3), find that you can get reasonable estimates with as few as 5 draws per observation when the number of observations is high.) ghk2() also speeds up computation for multi-equation ordered probit models. -cmp- now requires -ghk2-. The installation commands are "ssc install cmp, replace" and "ssc install ghk2, replace". Restart Stata after installing. As always, comments welcome. --David * * 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/

**References**:**st: Estimating total factor productivity***From:*Dadhi Adhikari <dadhinp@yahoo.com>

**st: RE: Estimating total factor productivity***From:*"Martin Weiss" <martin.weiss@uni-tuebingen.de>

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