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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

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

Subject |
RE: st: RE: fitting a gompertz curve, not in the context of survival analysis |

Date |
Sun, 31 May 2009 12:48:40 +0100 |

Thomas Love Peacock made some of his characters discuss this matter in his novel "Crotchet Castle" (Hookham, London, 1831). The entire text is easily accessible at e.g. http://www.thomaslovepeacock.net/Crotchet.html Peacock unerringly identified several key issues in your research, including the question of time origin. If you want to object that he supplied neither data nor precise equations that doesn't distinguish him from many of the economists who have discussed this matter since. On the other hand, the allusion to modelling is naturally prescient. In this novel of ideas, Mr Mac Quedy is, according to various scholars, based mostly on the Scottish economist J.R. McCulloch. Quedy is also identified as a play on QED, quod erat demonstrandum, i.e. on the a priori or deductive style of economising. What follows is an exact quotation from that URL, except that I have corrected "desert" to "dessert". (The Project Gutenberg copy is correct on that point.) Dr Folliott's reference to "your nation" underlines that he is English and Mr Mac Quedy is Scottish. As an Englishman with some Welsh antecedents married to a Scot, I want to underline that that difference is important. CHAPTER VI Theories But when they came to shape the model, Not one could fit the other's noddle. BUTLER MEANWHILE the last course, and the dessert, passed by. When the ladies had withdrawn, young Crotchet addressed the company. MR CROTCHET, JUN. There is one point in which philosophers of all classes seem to be agreed; that they only want money to regenerate the world. MR MAC QUEDY No doubt of it. Nothing is so easy as to lay down the outlines of perfect society. There wants nothing but money to set it going. I will explain myself clearly and fully by reading a paper. (Producing a large scroll.) 'In the infancy of society---' THE REV DR FOLLIOTT Pray, Mr Mac Quedy, how is it that all gentlemen of your nation begin every thing they write with the 'infancy of society'? MR MAC QUEDY Eh, sir, it is the simplest way to begin at the beginning. 'In the infancy of society, when government was invented to save a percentage; say two and a half per cent.---' THE REV DR FOLLIOTT I will not say any such thing. MR MAC QUEDY Well, say any percentage you please. THE REV DR FOLLIOTT I will not say any percentage at all. MR MAC QUEDY 'On the principle of the division of labour---' THE REV DR FOLLIOTT Government was invented to spend a percentage. MR MAC QUEDY To save a percentage. THE REV DR FOLLIOTT No, sir, to spend a percentage; and a good deal more than two and a half per cent. Two hundred and fifty per cent.; that is intelligible. <quotation ends> Nick n.j.cox@durham.ac.uk -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Dan Waldo Sent: 29 May 2009 15:52 To: statalist@hsphsun2.harvard.edu Subject: Re: st: RE: fitting a gompertz curve, not in the context of survival analysis Thanks to Maarten, Stephen, and Nick for very helpful comments. In particular, the -nl- suggestion was spot on ... I must have been experiencing one of those moments when you bypass the simple and go directly to the complicated. Nick asked about the tumor-growth reference. I confess up front that I got this from Wikipedia: Laird AK. "Dynamics of tumor growth." British Journal of Cancer 18:490-502, 1964. The model is nice in that it is expressed in terms of the change in tumor size (in my case, revenue as a proportion of GDP). Nick also expressed puzzlement over my intent -- a feeling that I often share. The hypothesis behind the work is that government revenue as a proportion of GDP is limited over time, either by political sentiment or by characteritstics of the evolving economy. Using the Gompertz curve is a simplification of a number of the things, and it could very well be that it so oversimplifies things as to become unworkable. Both Stephen and Nick asked about the natural time zero in this model, a point very well taken. I guess that one could establish as time zero the year in which the government were first created, if one were estimating the Gompertz function itself, although the analogy to tumors is a bit strong for my taste. But to take the time derivative of Laird's formulation (as shown in that Wikipedia article), I think that the time scale itself becomes irrelevant (not being a mathematician, I have asked a colleague to confirm this is so): dX(t) = a*log(K/X(t))*X(t) Unfortunately, this latter representation produces results that are inconsistent with the data, which could suggest that the model is not appropriate, or that my data are messy enough that the model cannot distinguish the "true" pattern. Estimating the function itself requires specifying a bae year, as Stephen pointed out. This estimation turns out to be exquisitely sensitive to the choice of base year and produces funky results, too -- leading me to think that the hypothesis is not borne out by the data. * * 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**:**Re: st: RE: fitting a gompertz curve, not in the context of survival analysis***From:*Dan Waldo <dan_waldo@yahoo.com>

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