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From |
"Thomas Jacobs" <thomasjacobs@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Setting up optimize for 2 equations in 2 unknowns |

Date |
Tue, 29 Jul 2008 17:48:42 -0500 |

Austin, Thanks very much for the reply. At least I can now get optimize to run. After a number of experiments it came down to its location inside the loop as you suggested. While I have not spent a lot of time with taking the logs or reparameterizing, I have found as you did that for many of my more difficult firms (those with high leverage and yet high equity volatility - pre-Fed bailout Bear Stearns is typical) the program with the default optimizer (modified newton-raphson) typically fails as a result of not calculating a numerical derivative. If I change the starting point for firm asset volatility from half the starting equity volatility to a proportion of the firms equity normalized by its assets it often does not converge (at least before I give up and hit ctl-break). Given that I coded a two variable newton raphson search in mata in my prior attempts at this problem, that while taking a long time for firms like Bear Stearns (thousands of iterations) always does converge, do you think the problem is that optimize() is only calculating one numerical derivative of the formula for sum of squares for each of the two variables where my newton raphson is calculating it for each piece (that is two for each of the two equations)? If so, is there a way to set up optimize() to separate the two equations in some fashion as opposed to working with their sum of squares? Thanks again for your time and thoughts. Tom On Mon, Jul 28, 2008 at 7:49 PM, Austin Nichols <austinnichols@gmail.com> wrote: > Thomas Jacobs <thomasjacobs@gmail.com>: > You may also want to reparametrize--I had trouble finding fake > starting values that would not crash your program. For example, if > Avol and AoX are always positive, try logs: > > clear all > mata > void Merton(todo, A, c, lnf, g, H) > { > f1=A[1]*normal((A[1]+c[2]*0.5*exp(A[2])^2)/(exp(A[2])*c[1])) > f2=-normal((A[1]-c[2]*0.5*exp(A[2])^2)/(exp(A[2])*c[1]))- c[3] > f3=normal((A[1]+c[2]*0.5*exp(A[2])^2)/(exp(A[2])*c[1]))*exp(A[1]+A[2]) > f4=c[3] * c[4] > lnf=(f1-f2)^2 + (f3-f4)^2 > } > T = 5 > sqrtT = sqrt(T) > X = 0.65 > E = 0.25 > Evol = 0.15 > Avol = ln(Evol/2) > AoX = ln(E + X)-ln(X) > EoX = E/X > c = (sqrtT, T, EoX, Evol) > S = optimize_init() > optimize_init_evaluator(S, &Merton()) > optimize_init_evaluatortype(S,"d0") > optimize_init_params(S,(AoX,Avol)) > optimize_init_which(S, "min") > optimize_init_argument(S,1,c) > B=optimize(S) > exp(B[1]),exp(B[2]) > * > * 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/ > -- Thomas Jacobs * * 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/

**References**:**st: Setting up optimize for 2 equations in 2 unknowns***From:*"Thomas Jacobs" <thomasjacobs@gmail.com>

**Re: st: Setting up optimize for 2 equations in 2 unknowns***From:*"Austin Nichols" <austinnichols@gmail.com>

**Re: st: Setting up optimize for 2 equations in 2 unknowns***From:*"Austin Nichols" <austinnichols@gmail.com>

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