Methods of Diffusion of Parent Relationships

1 Introduction

This document explores the four different methods for establishing firm-parent relationships.

  1. Cosigner Prior Adopter: the cosigner of deal when the firm becomes an adopter is a prior Adopter.
  2. Proximate Adopter: the firm who was a prior Adopter and most recently signed a deal with the firm before it became an Adopter.
  3. If the Proximate adopter is not available for a firm, then we use the Cosigner Prior Adopter as the parent firm.
  4. If the cosigner of the deal is not a prior adopter, then we use the Proximate Adopter as the parent firm.

Consider the following scenario. Firm 1 (F1), who is not yet an Adopter, signs a deal with Firm 2 (F2), who is an Adopter. F1 becomes an Adopter when they next sign a deal with Firm 0 (F0), who is already an Adopter at the time of signing. For F1, the Cosigner Prior Adopter is F0, while the Proximate Adopter is F2.

In what follows, we trace out the adoption patterns and histories of each method. The disconnected firms are not shown in these graphs.

2 Methods

2.1 Cosigner Prior Adopter Parent

Total Unique
Firm 76 76
Parent 42 30
Grandparent 14 11
Great-grandparent 2 2
Great-great-grandparent 0 0

D 3 3 51 51 3->51 167 167 3->167 215 215 3->215 45 45 215->45 6 6 91 91 6->91 131 131 6->131 140 140 6->140 9 9 85 85 9->85 196 196 85->196 10 10 5 5 10->5 77 77 10->77 139 139 10->139 21 21 5->21 112 112 77->112 246 246 49 49 246->49 64 64 246->64 16 16 49->16 26 26 52 52 26->52 29 29 52->29 27 27 29->27 32 32 8 8 32->8 63 63 8->63 34 34 23 23 34->23 44 44 94 94 44->94 198 198 44->198 50 50 141 141 50->141 55 55 162 162 55->162 53 53 162->53 61 61 58 58 61->58 285 285 61->285 104 104 58->104 84 84 285->84 125 125 285->125 69 69 84->69 66 66 31 31 66->31 60 60 66->60 70 70 186 186 70->186 73 73 152 152 73->152 87 87 79 79 87->79

2.2 Proximate Adopter Parent

Total Unique
Firm 76 76
Parent 47 23
Grandparent 31 7
Great-grandparent 17 3
Great-great-grandparent 7 1

D 130 130 61 61 130->61 44 44 61->44 50 50 61->50 58 58 61->58 86 86 61->86 2 2 44->2 3 3 44->3 9 9 44->9 15 15 44->15 32 32 44->32 51 51 44->51 52 52 44->52 84 84 44->84 92 92 44->92 91 91 3->91 167 167 9->167 9->167 131 131 32->131 136 136 32->136 16 16 51->16 8 8 84->8 152 152 92->152 10 10 26 26 10->26 28 28 10->28 53 53 10->53 69 69 10->69 119 119 10->119 66 66 26->66 60 60 28->60 85 85 28->85 162 162 28->162 49 49 69->49 141 141 69->141 246 246 69->246 45 45 5 5 45->5 21 21 5->21 59 59 63 63 59->63 137 137 59->137 23 23 137->23 215 215 137->215 73 73 23->73 115 115 18 18 115->18 6 6 43 43 6->43 47 47 6->47 198 198 6->198 125 125 79 79 125->79 77 77 132 132 77->132 46 46 196 196 46->196

2.3 Proximate Adopter Only If No Cosigner Prior Adopter

Total Unique
Firm 76 76
Parent 63 34
Grandparent 46 17
Great-grandparent 32 9
Great-great-grandparent 15 5

D 130 130 61 61 130->61 44 44 61->44 50 50 61->50 58 58 61->58 86 86 61->86 285 285 61->285 2 2 44->2 3 3 44->3 9 9 44->9 15 15 44->15 32 32 44->32 92 92 44->92 94 94 44->94 198 198 44->198 141 141 50->141 104 104 58->104 84 84 285->84 125 125 285->125 51 51 3->51 167 167 3->167 215 215 3->215 85 85 9->85 8 8 32->8 136 136 32->136 69 69 84->69 45 45 215->45 196 196 85->196 63 63 8->63 246 246 69->246 49 49 246->49 64 64 246->64 16 16 49->16 10 10 5 5 10->5 26 26 10->26 28 28 10->28 77 77 10->77 119 119 10->119 139 139 10->139 21 21 5->21 52 52 26->52 66 66 26->66 18 18 28->18 25 25 28->25 112 112 77->112 132 132 77->132 29 29 52->29 31 31 66->31 60 60 66->60 115 115 25->115 27 27 29->27 6 6 43 43 6->43 47 47 6->47 91 91 6->91 131 131 6->131 140 140 6->140 34 34 23 23 34->23 73 73 23->73 152 152 73->152 162 162 53 53 162->53 59 59 137 137 59->137 70 70 186 186 70->186 87 87 79 79 87->79

2.4 Cosigner Prior Adopter Only if No Proximate Adopter

Total Unique
Firm 76 76
Parent 63 32
Grandparent 47 14
Great-grandparent 30 8
Great-great-grandparent 13 5

D 130 130 61 61 130->61 44 44 61->44 50 50 61->50 58 58 61->58 86 86 61->86 285 285 61->285 2 2 44->2 3 3 44->3 9 9 44->9 15 15 44->15 32 32 44->32 51 51 44->51 52 52 44->52 84 84 44->84 92 92 44->92 94 94 44->94 125 125 285->125 10 10 26 26 10->26 28 28 10->28 53 53 10->53 69 69 10->69 77 77 10->77 119 119 10->119 139 139 10->139 66 66 26->66 25 25 28->25 60 60 28->60 85 85 28->85 162 162 28->162 49 49 69->49 141 141 69->141 246 246 69->246 112 112 77->112 132 132 77->132 59 59 63 63 59->63 137 137 59->137 23 23 137->23 215 215 137->215 45 45 5 5 45->5 21 21 5->21 79 79 125->79 91 91 3->91 167 167 9->167 131 131 32->131 136 136 32->136 16 16 51->16 8 8 84->8 152 152 92->152 115 115 25->115 73 73 23->73 18 18 115->18 46 46 196 196 46->196

3 Discussion

In conclusion, using only the Cosigner Prior Adopter gives the shortest family chains of only four generations, while the longest chain of eight generations is from using the Proximate Adopter only if there is no Cosigner Prior Adopter. The method with the greatest number of parent relationships is the Cosigner Prior Adopter, filling in with the Proximate Adopter, if the Cosigner Prior Adopter is not present. Using only Proximate Adopter gives the largest average number of children per parent. By comparing the firm history charts of these four methods, it is evident that firm relationships are path-dependent.