generalized preferential attachment model (gpmg)
TRANSCRIPT
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Generalized Preferential Attachment Model (GPMG)
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The goal of the model is to explain stylized facts
Assumption of the model
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(1) Sales distribution is skewedworld wide pharmaceutical database
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Number of products in the pharm firms
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(2) Growth rate distribution
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(3,4) average growth rate and its std.
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GPMG=Bose-Einstein + Simon + Gibrat
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First set of Assumptions
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(2-3) Bose-Einstein ; (4) Simon
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Second set of Assumptions (Gibrat Law)
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Pure Gibrat Model
Stilized Facts (2-4) are violated:(2) The shape of the growth rate is parabolic(3,4) The Growth rate and variance are independentof firm size.Moreover, variance grows linearly with time
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Pure Bose-Einstein: no new firms
Innovation parameter
Size distribution is Geometric
Number of active firms
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Growth rate is tent shape
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Stylized Facts 3-4 are violated
In reality =0.24
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Simon Model: new firms can be created
Finite time
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Finite time Behavior
Growth Factor of the Economy
New Firms : Crossover from power law for K<<R to exponential for K>>R
Old Firms
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Growth rate : disaster!
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Stylized Facts (3,4): Same as Bose.
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Full Blown GPMG
No analytical formula for the sum of Lognormals!!!
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Growth rate for Bose-Einstein
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Growth rate for Simon
Laplassian Cusp
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Size variance